I mostly play at game stores, but for home games my table isn't quite 36" wide. I went looking for options on how to make a good play surface without having to store a 36" x 36" sheet of plywood somewhere, and I found a solution that works really well for me: a tri-fold foam display board. It even comes in black, and it's $12 on Amazon.
The board comes as 36" x 48", but if you cut off one of the wings at the fold, the remainder is exactly 36" x 36". That leaves one folding wing (36" x 12") and the center panel (36" x 24"), and it was fairly easy to score the front of the center panel so it folds in half backwards. Then the whole thing folds down to 36" x 12" as a 3-panel accordion fold.
It's not the most durable, but it's light and cheap and folds down to a convenient size. It looks great with a play mat on top and not bad by itself, and it's easily stiff enough to support ships, dice, etc. as it hangs over the edge of a table.

I had a trifold board and I found the play surface to be extremely slippery. You bump a ship and it slides way too much. To stop that I put cabinet door bumpers on the bottom corner of each of my bases. I picked up a sheet of 48 bumpers for $3 or $4 (4 per base makes it 12 bases per sheet) and I picked up 5 sheets for under $20. No more slippy sliding.