i think u should get those plastic ones. i dunno watz it called but u can get it at popular or any store that sells stationery. they come in big sheets. there are "strips" of plastic in the middle to support the other 2 panels. they look like something i have drawn below. pardon me for my bad drawing skills. these kinda boards are a little tricky to cut though.
i wont reco foam. i dun knoe wat kinda foam u are planning to use but the ones i have worked, when u move any moveable part little pieces of foam will fall. can be quite irritating. however if u really want to use foam, i the best one would be blue foam (dun knoe watz its actual name but it comes in blue) its pretty dense. chances of it breaking up i alot lower than the normal white ones u see. btw the suction cups will diffinately not stick to the foam. not sure about the plastic though
hope this helps
cheers