Buccsfan64, welcome to the forum! Let me start by suggesting that, if you're using the white styrofoam that consists of a zillion little round pellets all bonded together into a sheet, you might want to reconsider. It tends to crumble when you work with it, and cutting and sanding leave you with a snowstorm of pellets and very rough, uneven edges edges. What I'd recommend is a sheet of extruded foam insulation. It comes in 4 x 8 sheets and has a fine texture---takes well to the knife and the sander.
Either way, you want to steer clear of any paint that is oil-based, as this will dissolve either foam product. Latex works fine, but ask for a non-oil-based latex, as there are a few oil-based ones. I've never tried to paint the white crumbly foam, but assume it's characteristics would be similar to the (pink, blue, or purple) extruded foam. That means one coat will do just fine, without a primer, once you peel off the plastic sheet.
Best wishes on your project!