I am designing a home theater that will have a small "stage" which will need to have a long (~8ft) piece of wood that is bowed slightly. I want to know what types of wood (e.g. MDF, certain plywoods, ect...) would be suitable for this task as I need to be able to bend the wood to shape.
I would say it should be around 6" wide at most.
I think MDF or a good-quality plywood would be perfect for this application.
To get the curve, you would cut a series of parallel kerfs in one side of the board, similar to the image below.
The spacing of the kerfs isn't an exact science, more of a trial and error thing.
As you can see, you only cut part way through the board. Ideally, if you use plywood, the ply you have left uncut has grain running perpendicular to your kerfs so that you're not bending across the grain.
I'm honestly not sure about thickness.
I would say your fascia board can be 3/4" thick and be fine. You would want to put another supporting board behind the fascia and under the stage pretty closely anyway to help carry the stage load.
Otherwise, if you want to get really complicated, you could use a solid hardwood and steam bend it the old fashioned way. Hickory, ash, and oak take bending well. See this related forum post for other woods. Air-dried lumber tends to bend better than kiln-dried, FYI.
For as light of a bend as it seems you're looking for, you might just be able to use several thinner boards (say 1/4" thick) and laminate them into the curve by gluing them into shape. It's fairly easy to make a jig to do this: