Where I live, 2x10s are pretty expensive. Structurally speaking, you could build the whole thing out of 2x6s with a single layer of 3/4" plywood and it would be plenty strong and rigid. I'd do a single box of 2x6 with short legs to get the proper height and wrap the sides with plywood for stiffness.
I'd also recommend using construction adhesive and screws (deck screws, not drywall screws) on the plywood decking. Joist hangers are a good idea, but put a little pad of roofing felt between the joist and hanger
This will also be more stable over time. Building it out of solid wood like you show increases the likelihood of wood movement over time, which will cause the joints to loosen and eventually start creaking and squeaking.
Good luck. This is a pretty straight forward project as long as you take your time and measure twice before you cut.
