@Logicfest -- if you have a modern desktop or laptop, you will probably have the specs you need unless you are doing professional, three dimensional stuff.
The problem with getting a good computer for animation is that putting all the pieces together can be a chore. What's the best CPU? How much RAM do you need? What about the graphics card? Do you need to get a better cooling system to deal with the increased heat your computer will generate when it's working hard to render those snazzy images?
Answering those questions (and more) requires a lot of research. There is a shortcut, though -- grab a gaming computer. A system that can handle the top of the line games of the day will be able to handle the requirements of a professional animation program just fine.