Soncino Talmuds are excellent.
Also you might want to get a large Hebrew English dictionary and a Jastrow (for Aramaic). This is just for a general introduction. The minimum level of learning everyone needs to get to in Talmud is to read and understand every Tosphot on the page and to be able to see the obvious questions.
The secret of Tosphot is that in every Tosphot there is some place that on the surface seems problematic. It is either a phrase or an idea that Tosphot introduces that seems to be out of place. It is in these spots that Tosphot plants the deepest ideas. (I learned to spot these areas when I learned with Rav Naphtali Yeger in Far Rockaway. Later when in the Mirrer Yeshiva in NY, I discovered that most people are not aware of the deeper aspects of Tosphot, but there there still was very high level of learning. But every person can discover this for himself if he is willing to spend the time on a Tosphot that is required. For people like me that is a lot of time. Like a week usually.)
Also, it is important to know that on every tractate there are one or two major akhronim (later authorities written after 1520) which are very important to learn. (Though I do knock the so called later authorities, but I am not referring to people that wrote on the Talmud itself. When I knock acharonim (later authorities), I am referring usually to people that wrote on halacha (like modern day pseudo halacha books). I would never dream of disparaging people like Rav Shach, R. Akiva Eiger or the Pnei Yehoshua (פני יהושע).
As for the Hidushei Ha'Rambam (חידושי הרמב''ם) of Rav Haim Soloveitchik, (commonly called חידושי רב חיים)-- it was the path of Reb Shmuel Berenbaum (of the Mir in New York). But this path has a great danger to it. It is easily misused by people that don't understand the Gemara itself. Quoting Reb Soloveitchik, or making up principles (yesodot) along his lines, provides an easy way for sounding like one knows how to learn (i.e. understand the Gemara). It is like giving a weapon into the hands of children.
So to learn Gemara you need to take just one Tosphot and learn it until you can answer these basic questions: What is Rashi saying? What is the Ri (R. Isaac) saying? Why does the Ri (R. Isaac Hazaken) disagree with Rashi. This is called learning. Most people skip this step. They think by jumping into questions of Reb Haim Soloveitchik that they can sound profound without understanding the basic page of the Talmud. And by skipping this step they are skipping something important for our day and age. Because inside of Tosphot is a whole sub-layer which does not get revealed until you start noticing small questions inside the Tosphot. This layer is something that people during the Middle Ages learned how to include in their writings without openly saying so.
If you have gotten to that step, the next step depends on faith. If you understand Tosphot, then you believe that there is a whole sub-level inside of Tosphot that you are missing. And you keep working and repeating the same Tosphot day after day. At some point you start noticing things that you did not notice before, and a whole sub-level opens up. [This last step can be really frustrating. Sometimes it happens when you notice that there are lots variables flying around in the Gemara that Tosphot is not mentioning but they make a difference when it comes to understanding Tosphot. But sometimes no. This last step is hard because there is no way to predict how long you have to keep on reviewing one Tosphot until something that seems simple you see starts to becomes complex.] If you absolutely can't spend this type of time on it, then at least learn the Maharsha and the Pnei Yehoshua (or the major akhron on that tractate. Like for Yevamot go to the Arukh LaNer.)-and then go on. (That is incidentally how I did it. I admit to get through Shas I could never have spent this kind of time on every Tosphot. But if one is not exposed to this type of learning at a young age, he never discovers this depth inside the Talmud. That is why at least some time has to be spent with people that can do this deep learning inside of Tosphot. The sad thing is they are hard to find. )
[If I could do so today I would have a separate session in Rav Shach's Avi Ezri word for word until I have finished the whole set. But in those early days, I was driven to finish Shas with the more basic people-the Maharsha and the early akhronim. And, I admit, I did not finish Shas with all those people. I got married and moved to Israel, and so the only tractates I did with most Tosphot and Maharasha were Ketubot, Yevamot and Shabbat.] [For example, on Nedarim there was ידות נדרים and for Ketubot and Yevamot I used the Aruch LaNer ערוך לנר. There is usually one major akhron [later book] for every tractate.]
Ketubot was basically done with the Maharaha, Tosphot, Pnei Yehoshua. Towards the end, I did a lot of Tosphot HaRosh because he would basically quote Tospohot, but with small differences. These small differences were a great help for me to understand Tophot, and the difference between Tosphot and the Rosh. I don't recommend this because it is just characteristic of my own mentality that I need some other commentary to put any commentary into perspective. This happens to me all the time. I can't understand Tosphot until I do the Maharsha. Then I can't understand the Maharsha until I do the Pnei Yehoshua etc.
[Traditional learning means to "calculate the sugia." This is very different that the Reb Haim path of finding yesodot (foundational ideas). Yesodot/foundations are ideas that the argument between people depend on. You find this in the Gemara itself quite a lot--when it asks what is the סברא logic behind certain idea.]
There are two approaches to Talmud. One began with R. Haim Soloveitchik. I must say that I did not learn this way personally. I heard countless lessons along the lines of Reb Haim. But when I got back to my shtender (seat), I plowed through the Talmud with the Tosphot and Maharsha and the early akhronim (like the Pnei Yehoshua). Sometimes I would go over and over a Pnei Yeshoshua about ten or more times until I got it.
But even this way could not be called traditional. The traditional way of learning was different. The principles were these: (1) Learn Tosphot. (2) It is forbidden to add any so called "principles"("yesodot") to make Tosphot make sense. He wrote it to make sense on its own. If you have to add outside concepts, then you don't understand it. (3) There is a point that you get to when you understand Tosphot that something comes up almost by magic. Some thought or question. It is that magical point that is called "learning." For me it is very hard to get to that point.
The way of Reb Hayim was different. He did add "yesodot" or principles, but from elsewhere in the Talmud itself. And he did it in a way that does fit.
If one wants to learn the best halakha book, the Tur with the Beit Yoseph is the best thing out there.
For Reform and Conservative Jews that don't have time for this, but still need a basic introduction, I suggest as I mentioned above to take one page of Talmud and do it with the Tosphot. After that you need to find the people on the page from this selection: Akiva Eiger, Reb Haim Soloveitchik [from Brisk], Rav Shakh. This will give a good basic introduction to what learning Gemara means. Of all the above, probably Rav Shakh's book, the Avi Ezri, shows in the most basic simple way possible what it means to learn Talmud. [I don't agree with skipping Tosphot. Not for anyone, and especially not for Reform Jews who have limited time to spend on learning Torah.]
[I also believe Physics is important but I do not have an system for it except what the Sages already wrote לעולם ליגרס אדם עא''ג דמשכח ואע''ג דלא ידע מאי קאמר "One should say the words in order and go on even though he forgets and even though he does not even understand what he is saying." And it has been noted before that learning Talmud with ethics (Musar) is important, for otherwise the whole point is lost and in fact has a bad effect. For the whole purpose here is to gain good character and compassion and fear of God. When Talmud is learned together with Musar, it has the above named effects. Without Musar it not only lacks this effects but causes the opposite traits. So I am definitely on board the idea of the Lithuanian Musar Yeshiva.]
Ideas in Talmud, Ideas in Shas Ideas in Tractate Bava Metzia, chapters 8 and 9 [For some reason you can not preview this book but you can download it.]
In these two books I am pointing to a new direction which I think learning Talmud ought to go. That is to concentrate on Tosphot. I feel Tosphot is simply ignored way too much. Or that people simply skip over something troubling inside of Tosphot without realizing the depths of what he is saying.
I would like to correct that. And in these two books I show the way to do this a little bit. But I highly regret I have not had time to write similar books on all of Shas. But I hope people will come after me that will continue this great work.
There is one basic yeshiva edition which is called the "Vilna Shas" It has no English and is the standard kind that they learn in all Litvak (Lithuanian) yeshivas like Haim Berlin. There are all kinds of modern editions which are no good. You have to be sure to get the right kind of thing.
[I might mention that my first reaction when I encounter a hard Tosphot is to look at the Maharsha. Also having a learning partner with a high IQ is helpful. Without either of these two aids, I really do not know what to do. The best bet is just to review the Tosphot every day without worrying about it too much. Just run through it. Maybe eventually it will make sense. In my two books on Gemara you will notice answers to questions brought up by my learning partner, but that is only because I had a learning partner. On my own I admit it is hard to even see what the issues are inside of Tosphot to even begin to think about them.]