Here's a quick update to my own post. I went to Home Depot and they only had Rustoleum sprays, which I decided to go with anyway because it was the cheapest stuff I could get. I got a can of white primer, a can of white gloss and a can of clear coat. Also purchased a trigger spray for ease and a wire brush for my drill.
I brushed the spotty areas down to bare metal, but didn't bother to do that for the entire frame. The rest of the frame, I just brushed down to remove the gloss and create a rough surface. Gave it a wash and dry, then sprayed it with 2 or 3 coats of primer. After it dried, I sprayed it with the gloss paint. I then cut out "SCHWINN" for the down tube and "WORLD" for the top tube to restore its identity. That's where I'm up to now.
I don't have a "before" photo because I got lazy, but here's what it looks like now.
schwinnworld..jpg
I'm rather happy with how it looks now. I'm going to let it continue baking in the heat wave after I hit it with the clear coat.
By the way, I did this outdoors in my backyard. I just brought it indoors for the decal work and photo. It shouldn't need to be said, but bring it OUTDOORS for spray paint work. Even then, I wore an N95 respirator and work goggles. After removing the respirator, I could still see a fading trail of paint trying to run down the side of my nose and into my nostrils. Glad I wore the mask.