half inch screws are fine. I guess something like 7/16 would be better but then you've got to find them.

You don't want to go any thicker than 1/2, or a lot of the stock mechs won't work.

I purchased some 'cabinet grade' 1/2" plywood from Lowes. My calipers put it at 0.48" thick. Without a source of 17/32 and a sander to bring it down to 0.5" I think that's your best bet (and my JD for instance still only measures 0.49")

I sanded the top lightly to get rid of the numbers, then sanded the bottom to get them flush with the wood

I've seen some pick up 5/8" baltic birch plywood that comes out closer to the real stuff (have not been able to find near me). I'm using 1/2" plywood and haven't had any issues with 1/2" screws poking through from below, but when mounting really thin stuff to the bottom I do have a supply of 7/16" screws as well. Any decent hardware store should have the 7/16", maybe even Lowes or HD. I think I did end up putting a thin washer spacer under my drop target mounts to get them to sit at the right height since the wood is thinner, easier to add spacers then take out wood.

There is a good overview here:

http://www.classicplayfields.com/standards.html