Hey Welcome to IS, I'm sure you'll get alot of good answers and how to's from your post.
I used 5/8 plywood on the floor of mine but I believe it's exterior grade. I got off a job site laying in the scrap pile
lucky for me. You would never believe how much wast there is on a big multi unit housing job
no wonder house prices are so expensive.
I put 2"s of blue foam on the bottom of the plywood and joined them together with some low expansion foam to form a tight seal. I also plan on water sealing the top of the floor as well as painting it with a good exterior paint with sand mixed in to make it non-skid.
your concern with the warping is caused when warm air forms condensation on the wood surface where it meets the colder air and is usually what makes the wood warp and with a shack floor, that will probably not happen any time soon
Good luck
FF