I’d probably go with a lower-profile 32-gallon trash can and a couple of sturdy, stackable plastic bins for recyclables. That should give you a good balance between capacity and keeping everything organized without taking up too much cargo space.
Another option worth considering is a heavy duty collapsible utility bin. You could keep it folded when you need the cargo area for other things, then open it up when hauling trash. For recyclables
,rigid storage totes would probably hold up better than the cheaper plastic drawer units and should be easier to clean.
The main thing I’d prioritize is something with a secure lid and a solid base so the bags don’t shift or leak during the trip to the dump.