I would use a short napped paint roller and regular old urathane. You will need at least 2 coats, probably 3 will do it, it might need 4. Lightly sand between coats, 200 grit after first coat and 200-400 grit after subsequent coats. The sanding after the first coat is because the first coat will "raise the grain". Any sanding after the second coat should be extremely light, just one or two swipes, then use either high pressure air and/or tack cloth to remove dust. Don't forget to give all four edges at least a coat or two to seal the door and prevent warping.