15/32 is just a hair under 1/2. I would go with something around 3/8 or even 3/4" for more support.. as for the grooves you can use a router with a fence on it and run your groove, you will have to do a few passes.

Or if you have a Dado blade, to put on your table saw, you can set the hight at what you want and then make a bunch of passes and adjust the fence as you go to make it the 11 1/2" wide you need. I've used both ways when building kitchens to get grooves. Good luck and post pics when you can.

Cheers