That’s a reasonable plan. 1/2” MDF or OSB would work fine if you don’t put to much weight on the over hangings, same with 1 1/2 or 2 inch foam board, but I would use 1/2” plywood.
Box home improvement stores often have pieces cut in 2’ x 4’ dimensions already for small projects. One side will be sanded nicer than the other
If you use MDF, plywood, OSB, any thing with wood, make sure you treat both sides the same, for example if you only paint one side it will warp. Paint both sides and weigh the surface down flat until the paint dries then do the other.
I’d get a table cloth of some kind to put under it, or even better some of shelf grip liner. Wood directly on wood will ruin your table.
The only other thing I’d worry about is your pieces moving once on the table. Probably the simplest thing to do is make only two pieces (I.e. 3’x4’) and tape the seam on the bottom with good duct tape.
Better would be to glue a piece of fabric tape, and staple it with wood staples.
Good luck, and feel free to ask questions.