For lightweight stuff, parallel should be fine. You may want to drill pilot holes, even though the ones I linked said they're self-tapping.

I recommended the "L" style instead of the hooks, so you could screw them in from the outside of the "cage" if necessary. Try to cut your plywood close to the inside size of the cage, so more of the shaft of the "L" hook is inside the plywood, not just a few threads.