You got the meaning of APO right (APOchromatic). As for how much of a 'must-have' it is, I think that at this point the biggest factor affecting how your photos turn out will be you, and the skills that you are able to develop.
If you ever intend to go further with your photography, you will want to upgrade to better glass, so worrying about APO vs. non-APO is kind of silly when you'll be eventually getting a better lens anyway. Personally, I think the softness that this lens is known for (especially at the long end) will be much more annoying/problematic than any chromatic aberration.
In any case, there are a lot of software options out there for removing
CA, although avoiding it in the first place would be better.
Learn with this (APO or non-APO Sigma, or any cheap telephoto for that matter) lens, and when you finally find that the lens is the limiting factor in your photography and it's time to upgrade, whether or not it is APO will probably be the least of your worries.
Dana