For hand drawn animation, you’re going to want one tool above all else: The Peg bar. It’ll keep your sheets of animation lined up so you don’t have any weird jitters when you’re shooting your animation. Just make sure you either order the right paper pre-punched, or you may be able to find the puncher cheap.
You’ll want something that will illuminate the paper so you can compare your last frame to your current one. This Page has a lot of useful information on different equipment, but before you spend the money on light table, you can actually use almost anything flat, translucent with a even light under it. My first light box was a tupperware container lined with tin foil that had a small desk lamp inside and a peg bar taped to the top.
None-photo-blue pencils are nice for getting the rough idea of what poses you want before you full on draw the character, and they won’t show up when you shoot the animation.
The most expensive part would be the actual filming of the animation. There are specialty camera set ups for this, but you can use almost any webcam if you can point it at a well lit surface that you can tape the pegbar to.
As for programs, that can be the expensive part. I’m partial to DigiCel Flipbook, but there may be alternatives out there. Anything that can take pictures and put them together in a sequence can work.