Thanks!
I would put the rabbet on the bottom piece, you'd have to make it .5" wider minus 1/32" to allow for wood movement. The rabbet should face down.
Then on the front and back, you can make a 1/4" groove about 1/4" from the bottom. I'd also break the hidden edges with sandpaper, so they do not impede with assembly nor catch. I'd also glue as such that none gets into the groove. You typically don't need to make the bottm piece shorter than the sides since wood would expand minimally if at all in that direction.