I want them to be waterproof, but I can't even imagine pouring a concrete slab myself. What are my options when it comes to building a shed with a waterproof floor that will stand the test of time?

Once the concrete has been poured, screeded and bullfloated, one man can easily finish a 10-by-12-foot slab.

From your description, we believe the plywood subfloor is fastened either to floor joists that are suspended above the concrete slab or to "sleepers" that are attached directly to the slab.