A major problem with GIFs are that it is a patent-encumbered format (EDIT: This is apparently no longer true). If you don't care about that, feel free to use GIFs. PNGs have a lot more flexibility over GIFs, particularly in the area of colorspace, but that flexibility often means you'll want to "optimize" the PNGs before publishing them. A web search should uncover tools for your platform for this.
Of course, if you want animation, GIF is the only way to go, since MNG was basically a non-starter for some reason.
