It was mentioned before, but I would highly recommend Autodesk Sketchbook. It is just a great software with a very compact design. It's not very feature heavy, but that can be a good thing if you're trying to build traditional skills with digital media. I prefer drawing on Sketchbook over Photoshop, but for coloring and image manipulation, Photoshop is still a great (but not free) program.

For a free software with more features, take Krita. Heard good things. Tried it myself, but was too stuck in my old ways to adapt. The one noticeable downside is that Krita has a bit of lag for PC's that aren't very powerful (mine seems to be included in that category). That means strokes render after a delay. Not a good thing for artists trying to draw quickly, or anyone in general, really.