Aerosol and foam board.

[Dewbakuk]

On-topic again; Will any hobby acrylics do, as long as the foam is covered?

Yes, as long as it isn't thinned too much. You want a proper coverage to prevent the solvents getting through. Obviously don't use little miniature paint pots, get some artist/craft acrylic to do it with.

[Captain Blood]

Sorry. Late to the party on this one 

I paint any bare exposed foamboard with PVA. This forms a nice skin over which you can spray the most corrosive enamel in the world, and your foamboard will remain intact. You do have to be sure to work the PVA into all the little dimples in the surface though, if you're using stuff like the Knaupf spaceboard, because the aerosol paint will find a way through any tiny un-PVA'd spots and eat away at the foam...

[Hammers]

Sorry. Late to the party on this one 

I paint any bare exposed foamboard with PVA. This forms a nice skin over which you can spray the most corrosive enamel in the world, and your foamboard will remain intact. You do have to be sure to work the PVA into all the little dimples in the surface though, if you're using stuff like the Knaupf spaceboard, because the aerosol paint will find a way through any tiny un-PVA'd spots and eat away at the foam...

I'm surprised that worked, Richard. In my experience PVA shrinks like a bastard and the lifting power may makes the board concave.

[6milPhil]

I also use PVA on edges or exposed foam, works fine for my needs...

[Captain Blood]

Yes, edges and bits and pieces of bare foam only.
I guess if you literally skinned the entire thing with PVA it would contract and risk warping. But along the edges and in dibs and dabs here and there, it acts as an excellent sealer and barrier to take aerosol enamel or primer...