Just my two cents, but here goes:
-First off, I would strongly recommend finishing both sides
of the piece. Next best would be to not finish it at all...but only finishing one side of a piece of thin stock is a recipie for warpage (Please don't ask how I learned that one!
-Alternately, you could saturate the piece (probably after most shaping/sanding) with water-thin CA glue...kind of a low-budget 'stabilization' alternative. This would help with the stability.
-Finally, the thickness might be determined by the pots/switch that you intend to mount on the piece...check them first, so you don't end up with a too-thick control cover.