Honestly, I started animating with paint. Yea, the cheap MS program on XP. I learned a few things not to do by trying to make video's and it taught me a few early tricks with each frame. The key things you need to animate is space to draw and be able to flip and compile the images quickly so that they look like they move. That's honestly it. I would just import all my images in movie maker and set them all to a high speed (.07 or .1 is the speed I put them at when I do something with the current live movie maker.)
GIMP and photoshop are better in that you can just create layers on top of another so that you can see what your first drawing was and directly be able to make changes. It also works well in real life with pieces of paper and a light box. That's a more accurate way to animate. Some programns like Toon Boom and Flash (actual animation software) work well because of 'Onion Skin', so that you can faintly see the drawing before and just draw the next frame slightly different. Honestly, you can animate with anything.