I would not use MDF board because of all the glues used to form it, which may be toxic. Likewise for chipboard. For a flat surface like a cage wall, plywood would be ok, but this shouldn't be used anywhere the hamster could realistically chew, such as for shelves within the cage. Solid, untreated, kiln-dried pine or spruce is safe to use anywhere, including for shelves, but not pine furniture board as this is laminated with some kind of glue.
Another option I thought of would be to get a glass tank and build a wood and wire mesh topper for it, using 6mm mesh. As I said, I'm not certain whether 6mm mesh would deter chewing, but it may. You could even use something like perforated metal which would definitely prevent chewing, but then it starts getting pretty expensive, and the skills needed are much more technical. I actually designed a front-opening topper recently for my gerbils (not built yet). It's designed to sit on top of a Kerry terrarium. Your tank could be more shallow for safety for a hamster. I've put a screenshot below to show the concept:
