Good quality 1/2" ply is really strong stuff. A combination of screws and wood glue will give you the strength you are needing.
Of course, you can always go exterior screw and not worry too much, the surface is easier to cover up on ply than mdf. Another blunt solution is big old lag bolts, They are not out of place, commercial cabs like the classic taito cabinet used lag bolts right out the side, and I always thought it still looked just fine.