A good place to start is http://en.wikipedia.org/wiki/Cartographic_projection Wikipedia. Read up on how projections work. It's also fun to check out various galleries online which showcase different kinds of projections.

Most computer programs that deal with projections (that I've used: g-projector, Flex Projector, Hugin has it as one of its projections) use as their base map a map in the Equirectangular, plate carree projection, which is very simple to compute (on computers). G-projector is the easiest to use, and now that it's upped its maximum output to 3000x1500 pixels it's much more useful.