When the Rambam mentions learning physics and metaphysics my feeling is that even though he says he is referring to how these subjects were understood in ancient Greece, I think you have to expand the definition to refer to Modern Physics and Metaphysics. But the later is harder to know. When the Rambam refers to Metaphysics that refers to the collected lectures in the book of Aristotle by that title. But nowadays I think you would have to include Kant and Leonard Nelson. Nelson started the new  Friesian-.SCHOOL; but even that needs modification as Bernays [one of his disciples] pointed out. 

[personally, I think it is a tragedy that Leonard Nelson is unknown.]

  Nelson was ignored, not from lack of quality, but from academic philosophy falling into the mud of analytic philosophy. They ignored real quality. 

  The fallacy of Analytic Philosophy is that analyzing language can not tell us anything about reality. It is hard to know smart people could fall into that. Analytic Philosophy is about as deep as a mud puddle. some people think that there are other approaches in philosophy after Kant that can replace Kant but i do not think that is right. 

I know there are people that think one ought to learn Torah alone, but that is more along the lines of the rishonim who held that way. But that is not the opinion of the Rambam or the Chovot Levavot.

[In Physics I suggest trying to get through every basic step from Newton until Einstein, Heisenberg, Feynman, and Susskind in the sense of "Bekiut" i.e. saying the words in order until you finish each book at least four times, and also listen to the lectures.