I built my cage with melamine boards, its chipboard with a plastic coating which makes the cage water resistant and easy to clean (
see here). If your cage doesn't have any edges that a hamster can chew into, a hamster shouldn't be able to chew through the wood, a hamster's teeth can't grip (and therefore crew into) a flat surface. I wouldn't use any type fiber board such as MDF board as its made from wood dust, it tends to bow easily and will swell if wet. You also cannot guarantee that the glue used is non-toxic. When using any kind of paint/varnish you have to make sure that it is a non-toxic, its best to use paint/varnish that is suitable for childrens toys. I personally use fiber glass anywhere near a pet cage. The fiber glass is, by definition, made from glass fiber which can get into the lungs and cause issues. The resin is also is also toxic and an irritent, the resin pretty nasty stuff.