My opinion here is to get a high grit sandpaper (220 or higher; 320 will better) and a foam sanding block and sand it by hand until all the major bumps are resolved. Then use a very thin filler to touch up and cracks or chips, and sand again with 320. If you are completely committed to a very high-gloss final look, wipe down the piece after that last sanding with a damp rag, cover it with primer in very light layers and take another look for imperfections. sand those down, prime one last time, and then paint the first coat. Wet sand the first coat when it has curedcompletely (spray paint - about 8 hours; other paint - according to the directions). "Wet sanding" means you're going to use a very fine sand paper (400 grit or higher) which is also damp to make your sanding as smooth as possible. Sand all the imperfections out of the first paint layer, and then paint again. Dry and wet sand again. Repeat, in fact, until you have 4-5 layers of fine sanding.
This process, when done with saintly patience, can give you a final surface as smooth as glass.
Good tutorial:
https://www.youtube.com/watch?v=RBENX1uvZak
