What boat are you building?
I built a plywood boat many years ago. My boat was actually the first customer completed Gatorboats Duckhunter.
Plywood will eventually check and when it does it allows water intrusion. Even if you painted it, the paint can separate/check with the plywood and allow water in. The best way to seal your plywood boat is marine 2part epoxy and fiberglass encapsulation.
Before you paint your boat, I'd recommend the following:
-brush/roll the entire interior and exterior with a couple of coats of two part marine epoxy. The plywood will soak up or "drink" much of the first couple of coats. Lightly sand between coats knocking down the raised wood grain and the epoxy "blush."
-Once you have coated the boat a couple of times, the exterior should get a layer of fiberglass cloth and epoxy.
-After fiberglassing the exterior, you can coat with multiple thin coats of epoxy (sanding between coats) until desired smoothness is achieved.
-One final sand and then paint as desired.
This doesn't mean you can leave your boat outside in the yearlong weather, but with proper care and storage it will last a long time.
Epoxy is expensive. I haven't price checked in a long time but back when I built my boat, this was the most cost effective epoxy out there. I bought my epoxy and fiberglass from this place. I used the 3:1 "medium" epoxy. http://www.uscomposites.com/epoxy.html