I use Kilz primer and any number of exterior house trim latex paints. I'd say most times it's Behr.
If you are using a furniture grade plywood (faced with oak , birch, etc), I'm assuming you are clear coating or staining and coating the piece. In that case, I would suggest you use a marine spar varnish (spar polyurethane) to finish the exterior surfaces. Standard polyurethane does not hold up well to moisture.
If you are not finishing with stains, and are going to paint the entire thing, then just get a quality exterior grade plywood with an A/B or A/C finish.