On my modules (for the club layout) I used 3/8" plywood over a 1 x 4 frame. They are pretty lightweight (I regularly carry one with each hand) and haven't warped or flexed much in the three years I've had them. They spend about 350 days a year in an unheated garage, so I think that's pretty good.
For a 42" wide area, I would add one center brace, so the longest span of plywood would only be 20ish inches. Before assembly, I would paint all the surfaces of the plywood (top, bottom, even the edges) to prevent moisture from causing it to warp. Might as well do the same with the frame while you have the paint out. A can of "oops" paint is really useful for this kind of stuff. Put two coats of whatever color you can find for cheap, and then do a finish coat of the color you like. For that area, most paint stores sell sample cans that hold about a cup of paint. Two would likely cover the top, and another one would probably do the sides of the framing that you will be able to see.
Even cheaper than the plywood is OSB. My Permanent layouts are made with 7/16" OSB, which is the same stuff most new construction roofs around here are made of so every lumber yard around has it. OSB has a smooth side and a rough side to it. I used the rough side on mine to give the paint just a touch of texture. (On a roof, you would use the rough side up so you don't slide off the roof, but that's another story...)
Hope this helps,
J White
