MDF is expensive and heavy, but very rigid, so will not need support. It comes in various thicknesses and gives a very smooth edge when cut with a power jig-saw. IMPORTANT: If cutting sheets of MDF, please wear a mask as the dust is dangerous.
4 MM PLYWOOD
4 MM Plywood is fairly rigid but will need supports at the back. For supports, use 2"x1" sawn timber (often called roofing laths). Use gloves when carrying to avoid splinters. Edges have to be well sanded down.
Hardwood is the cheapest of these three alternatives. It is surprisingly heavy but still needs supports at the back. Use the bobbly side to paint. Lay your sheets of hardboard down on the floor, touching each other in a series of tiles and seal them all at the same time. Only after they have been sealed and dried do you attach them to a frame and paint them. If you attach them to a frame and paint them before sealing them, they will warp.
Cardboard is cheap but hard to get hold of in large sheets. It can be fairly rigid but bends easily so it needs a frame support. To attach, use large- headed roofing-felt nails. Don't hammer these in too deep, as it will leave indentations that show even more under the top stage lights. You could cover with scrim or canvas to alleviate this problem. Use your paint as dry as possible.
Canvas is used for backcloths and simple flats i.e. those without profile edges.Canvas can be bought in huge widths from theatrical suppliers. It's cheaper if you buy it in the "standard" width of 9 feet and have it sewn. Normally a horizontal seam is a problem but if you use the "fence" to fall where the seam appears then it will hardly be noticed.