Garolite comes in many classes. G-10 and G-11 are probably what you want. 1/16 is a little thin, 1/8 is probably a min. You could get the thinest g-10 and glue it to both sides of some structural foam. Could also do it with some honeycomb material. This would give a strong composite board with out the hassle and mess of laying up a composite board.
Woodcrafters carries Baltic Birch.
http://www.woodcraft.com/family/2004113/plywood.aspx
What ever board you use, Get some nylon hardware to mount stuff.
http://www.mcmaster.com/#machine-screws/=v8em46