When we bought our home 6 years ago, the previous owners ran out of $$$ to do anything with the floor. They primed, then painted it yellow, and the wife stenciled around the edges with a nice, country stencil pattern (2 colors only; the floor was light yellow.) THen, when we bought it, we vinyled over it. Kinda like the situation we ran into.
Just get a good primer/sealer for the plywood. Use a semi-gloss, latex acrylic paint. If you need to put down 2 top-coats, then just do it. Depending on how long you intend to use the painted floor may not be worth trying to strrrrreatch 1 top-coat. Finnaren & Haley Primers + Paints are my favorite. Sherwin-Williams and MAB are fine too. Just stay away from the ones in the Home Centers, K-mart, and Wallmart if you know what I mean. THey stock the major mfgr's 'competitive models' in there. That's why they'er cheaper than the paint in the stores I initially mentioned. Look in the Yellow Pages under Paint - Retail and away you go. For the few extra $$$ you spend, it's well worth it.
My best to ya and hope this helps. Oh, no need to seal the paint. The semi-gloss should be fine. It will wear but that's because of the kind of paint you're using. As far as tiling directly over the paint, that depends. I'll leave that up to our resident Tile Experts to advise you on.