How to re-lacquer a vintage carrom game board

I recently purchased a vintage combination Carrom/Crokinole game board on eBay (the model 106, circa 1965-ish). Carrom and Crokinole are shuffle-board type games played with wooden or acrylic discs, about the size of quarter, on a flat wooden surface between 25 and 30 inches square.
The board was advertised as "Mint In Box" and it's obvious it has never been used before. However, the playing surface itself (on both sides of the board) is vey rough plywood -- it seems like there was never any lacquer applied to the surface (or if there was, it has long since dissipated). It's so rough, in fact, that the board is almost impossible to play on.
I'd like to know what steps to take to manually apply lacquer to both sides of this combo board. The purpose of relacquering would be to provide a smooth and slippery surface for playing Carrom and Crokinole. To this end, can someone answer the following questions:
A. What kind of lacquer is appropriate, given that the surface is plywood onto which the demarcation lines have been spray painted? I want to use a clear lacquer, but beyond that I have no preferences?
B. What kind of brush should be used?
C. How many coats of lacquer should be applied (I would guess at least three), and what (if anything) should be done to the board between applications (e.g. softly rub it down with steel wool, etc.)?
D. How long should I wait between coats (24 hours)? And what's the best way to minimize the risk of warping caused by applying the lacquer (e.g. should he apply coats to both sides of the combo board in the same session, or do each side on alternating days)?
Any suggestion, even anecdotal ones, would be appreciated as I am planning to refinish this board over the coming weekend. And please don't say: "You should let an expert do this!" I paid $11.00 plus shipping for the board, so I can only afford my own labor.
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Fact is, the original was also somewhat rough. I recall that I used steel wool and wax on the surface and the "vintage" was probably 48 or so. ANyway. I dont think you want to use brushed on lacquer. Either use steel wool and wax and then buff, or dilute polyurethane with naptha and brusg that and sand 220 grit before and between coats.
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