Wisdom of using Sympy as a first CAS

(I am the lead developer of SymPy)

I would recommend SymPy because it is in Python, which you will find is indeed a real plus. Also, in the past few years it's grown to be a very powerful computer algebra system, with some very fast, powerful, and nontrivial algorithms implemented. Also, in my experience, Maxima is slow (slower than both SymPy and most other alternatives as well).

Also, we have a great community if you need help :)

I recommand this online CAS calculator:

http://www.vroomlab.com/nhome

click on calculator image to access. No download/install!

it does algebra, trig, matrix, calculus. it is also a gaphing calculator.

this calculator is maxima based but can also use maple and mathematica as its CAS engine.

have fun!