I can buy a cheap skateboard for $20 US, but I would prefer to cut
my own. I do not want concave or springy, it needs to be strong
and lightweight flat wood. Anything readily available at the local
hardware stores that might work for a skateboard deck? Ordinary 1" x
8" (or 12") wood? Plywood?

There is a reason they use plywood. Get some Baltic birch.