I like Photoshop for painting stuff, and if you're just using it for free-form illustration, it probably can't be beat, but it's definitely not free. On top of that, it's not made for animation, though it can be used in a limited capacity for that. For a beginner at digital-everything-art, I suggest getting a pixel art tool made for pixelling to learn the basics of colors/contrast/clustering/materials/lighting/etc. Work at somewhat low resolutions to start with (48px-100px W and H at most), and shrink down from there. It helps to learn how to omit details from a high-detail model while retaining the characterization/lighting/materials/etc. This is a good start to getting you familiar with pixels.
As for specific pixel-art tools, you'd probably want to try Graphics Gale if you're interested in fast character animation. It's shareware, so it's free unless you want GIF support -- but, even without GIF support, you can still export a sequence of PNG images and use some freeware tool to stitch your frames together if you really want to make a GIF with the free version. Gale has its quirks, but it's an excellent tool made specifically for pixel-based art and animation. Spend a little time with its help file and learn some of its animation workflow shortcuts, and you'll be hooked. There's a lot hidden under the hood in this tool, and I almost passed it by til I learned about the way the rotate function and layer transparency work in relation to animation, and how rolling the mouse wheel goes through frames. Until you start animating pixels seriously, you wont realize how invaluable those features are.
That being said, if you're just painting pixels, pretty much any ol' program will do. Photoshop is very versatile, and there are neat tricks with it for pixel art, but it's got a high learning curve for new users and, as mentioned before, it's an illustration program, and it's not free, nor is it meant for animation. Bottom line is, choose what works for you. Do that, and you'll be all set.
