I must be the only one that likes using photoshop, haha. I've never heard of GIMP and some of these other ones, but photoshop has always worked for me and tons of other digital illustrators. There are plenty of tutorials and stuff out there, but eventually you'll find that you come up with your own method more or less. And there are ways you can acquire said program without depleting your wallet. *cough* pirating *cough cough*. Hope that helps!
That's not very specific. There's lots of software out there that does lots of different things. Even just within the category of graphics software, there is a lot of variation, for a wide sample of different kinds of graphics software, you could take a look at GIMP, Inkscape, FontForge, Blender, Hugin, and Processing.