Back to the original topic, I'll second the 1/4" deep dados, but I'd
also agree you'd want something other than MDF for your shelving
material. Solid hardwood (3/4") should be fine for 3', or even strips
of pine under MDF as supports should work.
Alternatively, if you didn't want to rout dados, you could cut a bunch
of 1"x1"xshelf depth" strips to use as cleats, and set your shelves on
those. You'd still need something to support the MDF in the middle,
but that's another option for the sides.
Good luck and have fun,