I'd wait at least 24 hours so that the paint is fully cured. If not it will be awful soft and even the dust can cause scratches.
If it were me, I probably wouldn't worry about going all the way back to the plastic, although you probably will in some spots anyway. Just get it nice and smooth, and clean up the panel lines and everything. If it winds up going all the way to plastic, so be it. If not, and everything looks good, just spray it again.
Finer grit paper is better, and going progressively from rough to fine is the best way. I'd probably start with 600 and end up with 1000 or 1200.