I'd stick with the brush.
Fitzy recommends "water based urethane", it's easy to get a very smooth finish.
The last ply board I made I used some gloss polyurethane I had in the shed. I got some granite laminex from one of the local kitchen makers, it made a nice shiny bottom, maybe a bit heavy and unneccessary though.
It was a pretty crap board, but made a nice coffee table!

It's most important to seal the edges of the ply. That's where it will soak up water.