If you're planning to make a career in 3D animation then 3DS Max is the way to go, along with Lightwave, Maya, SoftImage, ElectricImage and (possibly) Houdini. But be aware that they are only worth it if that is the way you want to go. Spending over a grand to just dabble in computer animation isn't really wise (although there are student editions available, but, of course you have to be a
student in a course involving 3D animation).
For the latter, I would look at Inspire by Newtek, who also produce Lightwave and the Video Toaster. Inspire is a cut-down version of Lightwave without some of the high-end features (no IK options, can't render images bigger than 640x480 for animation being two), but in other areas it is just as powerful. Also if you just want to have fun in doing character animation (Poser, is good but very limiting) there is Hash Animation:Master. The interface and modelling methods are not typical (it uses it's own form of patch modelling that is very different from other 3D packages but nice once you get used to it), and the rendering isn't great, but most of the things it can do can be found in high-end 3D packages. For instance it has its own form of non-linear animation, and a pretty good skin/muscle behaviour feature. You can also create fur and cloth with it (though they're not as good as they are in Maya).
Another package to consider is Cinema4D. It has quite a good range of animation features, is fairly easy to use and, more importantly, has a fast render (depending on the complexity of your creations you're going to end up waiting for ages when it comes to actually rendering them, so this is important). There are either Cinema 4D Go (cheapest) or Cinema 4D XL ($$$$).
Links for more info:-
Cinema 4D
Animation:Master
Inspire
Of course if you're even more of a cheapskate

there's always these:-
OpenFX
Blender