Is there a reason you can't just use a table? Hanging anything of value on a shelf suspended from hooks or brackets seems risky. Especially if people in the other storage nooks can accidentally (or on purpose) unhook things. I would either use something like a table, or two shelving units, facing each other, with a piece of plywood connecting them.

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.