I suggest staying away from proprietary systems like Mathematica or Maple.

What to use depends on what kinds of problems you need to solve. SymPy is really good for a lot of things, very simple to use, and just a Python library. Sage is more powerful in some areas (which may be irrelevant for your needs), but a much bigger beast. There are several old, powerful, clunky CASs like Maxima, Axiom, FriCAS, that you probably don't need.

I suggest starting with SymPy. Working on getting better at doing things by hand will be useful even if you mostly use a CAS in practice, since knowing how to do it by hand will mean you know what to tell the CAS to do.