120 and 220 grit to get the rust off to bare metal and feather the edge. 400 and 600 grit to color-sand the first few coats and blend them into the existing finish. When you get to where you can almost be happy with it, and the built up paint is about level with the existing paint, hit it with 800 and (optional) 1200 grit. After 1200 grit you're in liquid polish territory.
Almost all problems that can happen can generally be traced to either not starting with a cleaned (degreased, dewaxed) or badly sanded surface, or to trying to rush things and glopping the paint in.
So, we are almost there! I applied all layers, and I definitely got to remove the rust and protect the doors. Awesome. I do need to ring the clear coat down to the same level as the rest (it is a little higher than surrounding areas, and a little irregular. I am thinking sanding with a high grit? Or should I use a rubbing compound? I used one of those paint kits like in @nay 's post above. It's been 24 hours since I applied the clear coat. Is cured enough for smoothing it out?
Thank you all for great suggestions!