Reply by Jared_S

Not sure how you can make $400 work. You would need 7 sheets just for the uprights. At $60 per sheet for cheap 3/4 c3 grade birch or maple cabinet plywood you are already over budget.

Decent plywood won’t warp. Use 3/4 ply for the uprights and shelves. At least 3 fixed (permanently)shelves per vertical section with a 1/4” back and some 3/4 nailers. As stated the bottom will need a seperate 4” base or so to be able to tilt it into place.

2×12 construction lumber would be worse as far as warping.

3/4 or 1” poplar would be as cheap as possible if you wanted to go for solid wood that (should) be stable.