That will depend on whether it's a resin or filament print. Neither of them really need washing, but resin prints may occasionally have a bit of surface crud if it hasn't been fully washed out before curing — that's unlikely to affect paint adhesion though.
I always prime before painting. FDM prints can be slightly porous, depending on the print settings, and the sintered nylon prints you can get from Shapeways (I forget the name of that process) are like sponges. Both benefit from being sealed. Resin doesn't necessarily need to be primed, but I find it gives a better, less slippery painting surface.