Of all the issues with a projector going in an un-dedicated room, what material the stage is made out of is wwwwwaaaayyy down the list.
Your biggest issue visually, is going to be light reflection. Darker, less shiney, is better. Projectors are big bright things, the more light colored surfaces in your room for the light coming off the screen to bounce of off, the more your picture quality will suffer. Specifically the blacks will be washed out, colors as well to a lesser degree. The colors/surfaces directly surrounding your screen, IE floor, walls and ceiling, will effect your viewing the most.
There are a LOT of things you can do to help optimize a less than optimal situation, but basically its going to be a little bit of an, in for a penny in for a pound situation. If you're interested, I'm sure we can come up with a great list of things you could do to help create a better viewing/listening experience, but if that all sounds like work, I wouldn't worry about. I'd build your stage and cover it with whatever you like and get your screen and PJ up, turn the lights off and enjoy.
But, if you're like me (and a lot of others here) You'll find yourself wanting to tweak and optimize and play with everything here and there...the best bit of advice i can give you, is STOP, keep the PJ in the box, and do some planning first. You've already started asking questions, which is a great first step. But ask yourself what you really want from the experience and plan and budget accordingly.