what to mount my generator on

You don't need to put anything under a portable generator. You're going to have to wheel it outside to legally run it anyway. What problem are you trying to solve? Oil drips? Maybe try a piece of cardboard and swap it out from time to time, as you take the generator in and out for its periodic exercise.

You should be moving the generator outside to run it. It's in a well ventilated area in the mean time because of fuel fumes and such. Unless your floor is easily damaged (and it shouldn't be, it's in a shed), just park it directly on the floor. When running it, look for a level-ish spot. Concrete is great, but dirt or stone works fine, too...

I would use an anti-fatigue floor mat. The wheels will make divots into the squishy floor mat material and help it from moving around from the vibrations.