I need a suggestion for a floor in my house. The room is a second floor sleeping porch. Originally, this was an open balcony. Sometime around 1950 the balcony was enclosed, and an asbestos tile floor was installed on top of what looks like a rubber membrane. The balcony was not level because of water runoff. The tiles are coming off now, and need replaced with a different type of floor.

The floor mostly slopes away from the wall of the house, and from a high-ish point in the center. What type of floor should I put on this porch? I know I could do carpet fairly easily, but we don't really want carpet on a porch. Same thing with vinyl tile. What we really want is a wood floor of some type. How would I install it? There is no sub-floor. Would I have to lay down plywood? Floor leveling compound? How would I attach the new floor without there being a sub-floor?

Let me know your advice. The house is 1917; the dimensions of the porch are 8 x 17.