\What is the best way to frame a box?
Isherwood's answer is great, however, I'd question why you are using lap joints at all if that's the type of vertical you are thinking about.

It's far less work to not bother with the lap joints and just tie the sides directly into vertical posts like this:


However if you insist on using lap joints I'd say you want every face to have to be made of it's own lap jointed rectangles, them just link the rectangles together so it looks a bit like this (imagine the top part of the frame with less overhang):