how thin are we talking? 1/8" is very readily available as plywood. I have been using that and it doesn't warp, or at least not for me, not yet. MDF can get thinner yet with specialty orders but if you are ordering it you might as well stay with plywood as that can get even thinner. From there, you can do drywall plaster. There is 2 very different types both very available from Lowes or Home Depot. The stuff used just for patches is cheaper and weaker but im sure would do the trick just fine.
The only tools you would need is the right jig saw and a sander. I have yet to do any large warmaster terrain pieces so I don't know if I am of good help.
I have gotten some plastic card from litko.
http://www.litko.net/I buy bases for my heroes from them, round micro-plywood, I buy them without the magnets but only because I use magnet sheets for other things so I have plenty of scrap left over and cutting to size after glueing is really easy.