This is what I used for my tea boxes which have 3/8" walls and a 4" wide top.
All the slots are 1/8" (TS rip blade kerf) For 3/8" thick walls....
Raise the TS blade 3/8". Cut the kerf with the blade set 1/8" from the fence around the perimeter of the lid, inside surface against the fence.
Without moving the fence, lower the blade to 3/16" or 1/4" (wall dado depth) and cut the groove along the top inside edges of the walls.
Trim off the lids tongue to 3/16" (for 3/16" depth dados) or 1/8" (for 1/4" dado) in from the edges of the lid.
The sides are then positioned 1/8" or 3/16" out from the walls outside faces for the top reveal and the gap in the dados for wood movement.
The walls that meet the lids end grain can be glued with a dab in the center of the slot and seated fully on the lids tongue. If you glue these ends so they are centered on the lid, you then can just assemble the rest of the box knowing the lid is centered side/side and front/back with the maximum room for expansion or contraction.
