Reb Chaim [Soloveitchik] and the the Avi-Ezri

There were four people in pre World War Two Europe that had the best understanding of the Torah.
They were Reb Chaim [Soloveitchik], Reb Naphtali Troup, Reb Baruch Ber, and Reb Shimon Shkop.
I would rather not go into the issue of why expertise in Talmud makes one an expert in Torah at this point.
That is a worthy question but it is not the question I want to address right now.
[Simply the major reason is that the Talmud is a rigorous examination of the Torah in the most logical powerful way possible. Talmud does not claim Divine inspiration. It does however try to determine what the Torah requires from people,  and how to go about keeping the commandments of the Torah. It is not a conspiracy to uproot the Torah, but rather an extreme  and rigorous evaluation of the verses of the Torah in order to best understand what God wants us to do in life. It does not claim authority for itself to interpret and verses. Its sole claim is that reason alone is qualified to understand the Torah, and who ever reasons better- wins.]

But it was specifically  Chaim Soloveitchik that concentrated on understanding  the Rambam and how his opinion flows from the Talmud. [The Chidushei HaRambam of Reb Chaim is thus the kind of Tosphot that the Rambam would have written to explain how he derived his result from the Gemara.] And after him his two students worked on continuing this effort, (Baruch Ber and Shimon Shkop). This was definitely a revolution in Torah thought. After that came Elazer Menachem Shach with the incredibility deep book, the Avi-Ezri. I learned  under Shmuel Berenbaum who in some way was a continuation of this school of thought, but applied the Brisk method to the Gemara itself. I have long wondered why no one seems to have put down his classes in writing? For I think he had some very important insights into the Gemara.
[Towards the end of his life they taped his classes. But they were deep, and also in Yiddish. I can see some of the problems involved in publishing his ideas.

To understand the Rambam on the surface level is what the commentaries were doing before Reb Chaim Soloveitchik. For example the Rambam might say a certain Halacha, Then the Magid Mishna or Keseph Mishna will point out that he is going like the principle Shmuel in dinim (civil law) and like Rav in isurim (prohibitions). The trouble is that in Shas, there are about ten major ways of deciding Halacha. There is: (1) the order of tenaim in Eruvim. (2) We have: "Student against his rav (teacher) , the halacha is like the rav." (3) We have: "stam Mishna." [The Law goes like an anonymous Mishna.] (4) We have "majority," etc.(5) "Rav and Shmuel the law like Rav in Isurim and like Shmuel in Dinim/monetary issues. Take any principle and apply it to any halacha you will get a completely different halacha. Plus לישנא בתרא which is how the Rambam and Rif always decide is itself subject to argument. Some Rishonim hold you always go by the first לשון. Some by which ever is more strict in Torah din and less strict in derabanan. I could go on, but you get the idea.

These are vast and hard problems and the beginning of the effort to deal with them comes from Reb Chaim Soloveitchik. This effort was mainly crystallized in his book and his two students Barch Ber and Shimon Shkop and later in the Aviezri by Rav Shach. The most readable of them is Rav Shach's book, and I think it is also the best of them all.
So the best idea is the get the basic set, Rav Shach's Avi Ezri Reb Chaim's Chidushei HaRambam, plus the basic set of the classical Musar books along with Reb Israel Salanter's disciples  and you are all set for launch.

[In a side note: I would suggest in terms of Halacha the Tur and Beit Joseph as the best halacha book out there.]
The Rambam is not infallible. No one says he is. In the Guide he says Aristotle is right about everything under the orbit of the Moon.  He did not for some reason see that what Aristotle wrote about circular motion made no sense.

Here is what Dr Steven Dutch writes about that:
The ancient Greeks weren't trying to be us. They didn't know our sort of world was possible. In many cases they were trying to answer the big questions: what is motion? What is cause and effect? It wasn't at all clear that meticulous observations of commonplace natural phenomena would lead anyplace. Add to that the pervasive disdain for manual labor that permeated the intellectual community pretty much up till the time of James Watt, and it's not hard to see why they didn't develop science as we know it. But the clearest exposition of the fatal conceptual errors the Greeks made is probably in Aristotle's On the Heavens. Quotes are from The Internet Classics Archive.
Book I

Part 1

A magnitude if divisible one way is a line, if two ways a surface, and if three a body. Beyond these there is no other magnitude, because the three dimensions are all that there are, and that which is divisible in three directions is divisible in all. ... We cannot pass beyond body to a further kind, as we passed from length to surface, and from surface to body. For if we could, it would cease to be true that body is complete magnitude.
We're not off to a very promising start. Aristotle can certainly be forgiven for assuming there are only three spatial dimensions. Even modern scientists and mathematicians have trouble thinking about higher spatial dimensions, even though we can do the mathematics perfectly well. Aristotle could have taken three dimensions as given, or he could have tried to work out the implications of more dimensions and then argued that we don't observe those phenomena.
Instead, he commits an elementary fallacy - a circular argument. There is nothing else beyond body (three dimensional solid) because if there were, then there would be something else beyond body.
Part 2

It's in Part 2 that we may find the clearest exposition of how ancient science went wrong.
"The question as to the nature of the whole, whether it is infinite in size or limited in its total mass, is a matter for subsequent inquiry."
Good move. An impossibly turgid discussion of this topic makes up much of the early part of his Physics.
"We will now speak of those parts of the whole which are specifically distinct. Let us take this as our starting-point. All natural bodies and magnitudes we hold to be, as such, capable of locomotion; for nature, we say, is their principle of movement."
I guess there's no harm in assuming everything is capable of motion, but there is also no deep conclusion to be drawn, either. By linking motion to a "principle," that is something inherently linked to matter, Aristotle has waded knee deep into a morass.
"But all movement that is in place, all locomotion, as we term it, is either straight or circular or a combination of these two, which are the only simple movements. And the reason of this is that these two, the straight and the circular line, are the only simple magnitudes."
Now he's waist deep. Yes, you can describe all motion as a compound of linear and circular motion. For that matter, vectors treat all motion as combinations of linear motion. And it makes sense to do this kind of analysis because lines and circles are easy to analyze. But that's solely a matter of mathematical convenience to us. It says nothing at all about the kinds of motion that exist.
In his Physics, Aristotle devotes much effort to distinguishing properties that are "essential" from those that are "accidental." Having weight is essential to a stone, being red is accidental. The stone could just as easily have been gray or black. Aristotle's fundamental mistake here is failing to realize that the geometric description of motion is accidental, not essential.  The shape of an object's path is wholly dictated by external forces. The motion itself has no other meaning. A stone in a sling moves in a circular path solely because the sling is the radius of a circle, and the motion itself has no other significance. In fact, all motion itself is accidental. A stone might be at rest on the ground, or in linear motion because you throw it, or in circular motion because you are slinging it.
We have now encountered the two chief fallacies that derailed Greek science, and the whole Western world, for that matter:
Motion is an inherent property of matter.
The geometry of motion has special properties.
"Now revolution about the centre is circular motion, while the upward and downward movements are in a straight line, 'upward' meaning motion away from the centre, and 'downward' motion towards it. All simple motion, then, must be motion either away from or towards or about the centre. This seems to be in exact accord with what we said above: as body found its completion in three dimensions, so its movement completes itself in three forms."
If "up" is away from the center, and "down" is toward the center, then Aristotle must have believed the earth is a sphere, right? Yet another demolition of the myth that people in ancient times thought the earth was flat.
And Aristotle comes this close to drawing the correct conclusion about motion in three dimensions. A rock has three dimensions because it has length in a vertical direction, from right to left, and from front to back. Motion has three dimensions because something can move in a vertical direction, from right to left, and from front to back. Instead, he falls back on numerological mumbo jumbo, classifying motion as circular, upward, or downward to get his mystical three. His failure to consider horizontal motions has enormous negative ramifications for science. Actually, he comes so agonizingly close. If circular motion is motion about the center, then motions parallel to the surface of the earth are actually circular, which means they must be the same as circular motions in the heavens. He could have avoided the false dichotomy between celestial and terrestrial that burdened science up to the time of Galileo, but he muffed it. Now he's chin deep in the swamp.
"Bodies are either simple or compounded of such; and by simple bodies I mean those which possess a principle of movement in their own nature, such as fire and earth with their kinds, and whatever is akin to them."
Now he's in over his head. We have come 777 words in the translation used here. It has taken Aristotle a mere 777 words to shunt science off onto a dead end that we won't extricate ourselves from for close to 2,000 years. He has assumed there is a fundamental link between matter and motion, he has assumed the geometry of motion has special properties, and now he's assuming that certain materials inherently possess motion as a property. All of it completely wrong.
"Supposing, then, that there is such a thing as simple movement, and that circular movement is an instance of it, and that both movement of a simple body is simple and simple movement is of a simple body (for if it is movement of a compound it will be in virtue of a prevailing simple element), then there must necessarily be some simple body which revolves naturally and in virtue of its own nature with a circular movement."
Rephrasing: Supposing, then, that there is such a thing as simple movement [there isn't], and that circular movement is an instance of it [it isn't], and that both movement of a simple body is simple and simple movement is of a simple body [these don't even rise to the level of being false - they're simply meaningless. What he appears to mean is that if a motion is simple - linear or circular - then the body with that motion must be simple.] (for if it is movement of a compound it will be in virtue of a prevailing simple element) [Except when the body isn't simple after all], then there must necessarily be some simple body which revolves naturally and in virtue of its own nature with a circular movement [non-sequitur].
We can see the groundwork being laid for the geocentric picture of the Universe, with the heavenly bodies having inherently circular motion. All based on a grand non sequitur. Just because a type of motion can be said to exist doesn't mean there must be a body which possesses it.
"By constraint, of course, it may be brought to move with the motion of something else different from itself, but it cannot so move naturally, since there is one sort of movement natural to each of the simple bodies."
Talk about a missed opportunity. If, say, a stone in a sling has circular motion only by constraint, maybe allcircular motion is by constraint? Maybe the planets move in circles only because they're constrained?
"Again, if the unnatural movement is the contrary of the natural and a thing can have no more than one contrary, it will follow that circular movement, being a simple motion, must be unnatural, if it is not natural, to the body moved."
Motion is unnatural unless it is natural. We can see why philosophy has been regarded as the pinnacle of human intellectual endeavor for thousands of years. And what says something can only have one contrary? Saying Milwaukee is the capital of Wisconsin is the contrary to saying Madison is the capital, but so is saying Green Bay, or Sheboygan, or Superior is the capital.
"If then (1) the body, whose movement is circular, is fire or some other element, its natural motion must be the contrary of the circular motion. But a single thing has a single contrary; and upward and downward motion are the contraries of one another. If, on the other hand, (2) the body moving with this circular motion which is unnatural to it is something different from the elements, there will be some other motion which is natural to it. But this cannot be. For if the natural motion is upward, it will be fire or air, and if downward, water or earth."
I bet Aristotle never went fishing. Everyone who's ever gone fishing has been confronted with a snarl where, the more you try, the worse it gets. The only cure is to cut the mess off and start over. Aristotle is hopelessly snarled here. He's way over his head in the morass and sunk deep into the mud on the bottom. Having already erroneously decided that he knows what kinds of motions exist, and what sorts of matter naturally possess what kinds of motion, he just keeps piling wrong conclusions one atop the other.
"Further, this circular motion is necessarily primary. For the perfect is naturally prior to the imperfect, and the circle is a perfect thing. This cannot be said of any straight line: not of an infinite line; for, if it were perfect, it would have a limit and an end: nor of any finite line; for in every case there is something beyond it, since any finite line can be extended."
Even in Aristotle's day, this was simply nonsense. A circle and an infinite straight line are the only two simple forms that are self-similar, that is, any part is like any other. We now know of self-similar fractal forms, but we can forgive the ancient Greeks for not knowing. However, an infinite straight line has the property that every portion, whatever its size, is exactly like every other portion. You can't say this about circles. Any 10-degree arc of a given circle is like any other, but it's not like a 10-degree arc of a different sized circle, nor is it like a 20-degree arc of any other circle. A millimeter of an infinite straight line is exactly like a segment a light year long. Aristotle says an infinite line can't be perfect because it has no end, and a finite line can't be perfect because it has an end.
Clearly, Aristotle has some sort of mystical attachment to circles. And another golden opportunity goes by. Because if he'd decided straight lines were the perfect form, he might possibly have groped his way to the concept of momentum and Newtonian physics.
Here we go. Road map to the Middle Ages.
"And so, since the prior movement belongs to the body which is naturally prior, and circular movement is prior to straight, and movement in a straight line belongs to simple bodies-fire moving straight upward and earthy bodies straight downward towards the centre-since this is so, it follows that circular movement also must be the movement of some simple body."

"For the movement of composite bodies is, as we said, determined by that simple body which preponderates in the composition. These premises clearly give the conclusion that there is in nature some bodily substance other than the formations we know, prior to them all and more divine than they."
Not a single premise in that paragraph is true and not a single statement follows from any other:
And so, since the prior movement belongs to the body which is naturally prior [Tautology, and meaningless]
and circular movement is prior to straight [false]
and movement in a straight line belongs to simple bodies [false]
fire moving straight upward and earthy bodies straight downward towards the centre [true observations, false implication, that there is only one center]
since this is so, it follows that circular movement also must be the movement of some simple body. [complete non-sequitur]
For the movement of composite bodies is, as we said, determined by that simple body which preponderates in the composition. [false in too many ways to list]
 These premises clearly give the conclusion that there is in nature some bodily substance other than the formations we know, prior to them all and more divine than they. [The Grand Non-sequitur]
At any rate the evidence of all other cases goes to show that it is the unnatural which quickest passes away. And so, if, as some say, the body so moved is fire, this movement is just as unnatural to it as downward movement; for any one can see that fire moves in a straight line away from the centre. On all these grounds, therefore, we may infer with confidence that there is something beyond the bodies that are about us on this earth, different and separate from them; and that the superior glory of its nature is proportionate to its distance from this world of ours.

So there we are, locked to the notion that circular motion is inherently superior and that bodies that possess it must be inherently superior as well.