Actually, Floyd86 raises an interesting point. Anim8or certainly will run very well on older, basic machines, due to it's very low impact on machine resources, but even if you planned to use no other 3D package you would still be better off getting the most powerful machine you can afford. Let's face it, probably 50% of the actual work involved in creating an original animation is done outside Anim8or, with 2D graphics platforms for texture manipulation, UV unwrappers, web software, video editors, audio processors and multitrack recorders, etc. Many of these will have a much greater demand on resources than Anim8or.
Really, in my opinion, the only place you can save money when buying or building a computer is in the case! Get a basic enclosure without flashing lights and peek-a-boo windows and pack it full of serious goodies. You can also save a bit initially by going for a smaller internal hard drive, you can always add more with a RAID setup or a bunch of USB drives as you need them. An 80GB internal drive is WAY big enough for Windows XP (not sure about Vista) and all the software you will need, if you dump your files to an external drive (my own internal drive is a slightly embarassing 20GB, which holds ALL my software, though I have an extra 2TB in USB drives for file storage).