jgedwa, I kind of agree, except that he wants to paint his bike, and there's not much to lose. It's not like learning to paint on a better frame would make more sense. This way, he gets to learn how to do it, including the mechanical parts that will be necessary.
Joshman, painting metal, particularly metal that's going to get a fair amount of wear and tear, is no mean feat. If you're going to rattlecan it, you'll really benefit from stripping all the parts off. Mask the brake bosses and anything else you can't get off.
Absolutely, without a doubt, remove:
Wheels
Chain
Bars
Stem
Cranks and chainwheel
Derailleurs
Brakes
Seatpost
Cables
You can mask the headset and bottom bracket, but I'd remove them, myself.
Then go over it with very light coats of spray paint, leaving at least a day between coats to dry in a warm, dry area. If you don't live in a part of the world that is currently warm and dry, do it in a few months.
I should be clear: it's kind of a big job to do yourself. You'll need to get bike tools to do the dismantling if you don't have them, and Roadmasters aren't made to be dismantled; they're made to be used and thrown away, so stuff may wind up breaking as you take it apart.
I painted a frame (A Trek 7300 aluminum frame) a year and a half ago. It's got some chips, but it still looks OK. It's a long way from the factory-like finish my Cannondale has from the $75 powder coat I got on it.
(As far as I know, the only difference between painting an aluminum or steel frame is that you have to look out for the steel rusting quickly once you get the paint off. Don't leave it around overnight in a damp place or anything. Strip it and paint.)