For what you are doing, I would buy a can of Zinnsser 123 Primer for about $20 a gallon. I would get a 4 inch roller and use a foam roller for a smooth finish. It dries pretty quickly. Since its wood, I would do a second coat of primer. Put the roller in a plastic bag and wrap it tight after you use it the first time, and you can use it over again for the second coat. I do this for painting jobs that last all week!!!
Then I would hit it was a palm sander, or just a block of wood and sand by hand with some 100 grit paper. Sanding will take two minutes. You just smooth it out and it will be like glass.
I would not use a sprayer because of all the time it takes to clean the sprayer. It's also more money for Paint Thinner to spray it, and Lacquer Thinner to clean the sprayer.
Just swinging back around to this. Eddie what you described is pretty much my exact process, except I've been using a high quality, angled bristle brush and an orbital with 220grit (better cutting control).
Slowly spooling up to start another enclosure for when I get caught up on everything else at work. Picked up a 4" foam roller and I am also going to try the bondo trick someone else suggested for sealing/smoothing the edges of the plywood.
That being said, I do want to pick up one of the Harbor Freight $15.00 purple, gravity feed guns and some Floetrol to play with sometime down the road. Apparently folks have good success boring out the nozzle to 2.0mm for running primer. I really really am appreciative of the concept of being able to prime both sides in one go and I enjoy experimenting. Once college starts back up in the fall, I'll have no shortage of interns to help with the cleanup.