Don't do one thick coat or you will regret it... it may not fully cure if you do this and you'll make a mess when trying to sand flat... I'd do multiple thin coats, and let each one cure. I use small plastic pipettes for dripping varathane and or sucking air bubbles back out once you've dripped the liquid. You'll want let the top coat fully cure because it will require some serious sanding to flatten the varathane without hosing the surrounding playfield art. I use low tack paper tray liner to protect the playfield when sanding (cut round circles in the liner that allow full insert sanding only).
Tons of helpful info on pinside on sanding paper, grit, other methods, etc. I performed this method on a Bally Expressway many moons ago ... came out great.