I’m using leftover plywood for boxes also. You don’t want any of the end ply exposed on the corners. I’m using miter joints with dovetail keys on mine.
Using CNC you might be able to get more creative and use blind dovetail miters or tongue and groove miter.
Another very cool option that will extend the life of the box is to cut mitres through all but the last ply, which is then folded giving you a continuous layer of wood around 3 of the joints.
Here’s a link to a single piece of wood miter: http://www.popularmechanics.com/home/interior-projects/a15537/cut-makes-building-drawers-super-easy/