I plan to install 3/4 inch Brazilian cherry hardwood (3 and 1/4 inch width) over concrete on our first floor. I do not believe we have a moisture problem but will test. I would like to use a floating floor approach with two layers of plywood sheets applied in opposite directions and screwed together. I plan to use plastic sheeting as a vapor barrier between the plywood and the concrete. What do you think of this method? Between the plywood and hardwood I will have a height issue and would like to know how thin I can go on the plywood, 3/8ths or 1/2 inch?

Two sheets of 1/2" plywood is the recommended way of installing a floating subfloor. They are installed 90 degrees to each other and are scewed and perhaps glued as well, together. The 6 to 8 mil polyethylene plastic vapor barrier is installed on top of the concrete and underneath the plywood. Do not use plastic sheeting between the two plywood panels. Some wiggly beads of solvent based construction adhesive along with the short screws is all you'll need to attach the panels to each other. After the plywood is installed, a layer of #15 lb. aspalt saturated felt is recommended on top of the subfloors and under your wood flooring. I'm afraid 3/8" is a little too flimsy. You would have a difficult time getting that together very flat. The 1/2" will be hard enough to keep flat.

Thanks. Sounds like good advise. As an alternative would you recommend screwing down 5/8ths inch plywood to the concrete floor with the same vapor barrier? I am a bit reluctant to use this approach as the floor is very wavy and I thought the floating floor would give me better tolerance.