I'd install 5/8" plywood. Install it PERPENDICULAR to the subfloor. Also, chalk-out where the subfloor is nailed to the joists, and transfer the location to your NEW plywood. I'd screw the new floor down. You want the screws to go at least 3/4" into the joists. So you'll need 2" screws. Pre-drill them first with a 3" drill bit. You'll have to cut your doors a bit too. You may not be able to do this yourself. And you may have to cut the door's trim too.
Use a Primer / Sealser from a reputable Paint Retailer (found in the Yellow Pages under Paint Retailer) for the Primer/Sealer (a 2-in-1 product.) Be generous. Then paint with a durable paint that will handle foot traffic. Bordering out the room in a stencil would be a nice touch! And put down at least 2 coats of top-coat paint. Do talk to the Retailer and describe to him/her what you're doing. They may have more questions.