I second Plethora's excellent advice.
I wanted to add that with your art background you may find the following free programs useful:
GIMP is a great program for 2d raster artwork (although some prefer Paint.NET). Inkscape is a great tool for vector based artwork. Blender is good for a whole lot of stuff including creating 3D models for games. Synfig is a good vector animation package (and there is a plugin to export from Inkscape into Synfig.).
You might also like:
Shoebox is good for working with sprite sheets and Pencil is good for prototyping GUIs.