The inner dimensions of the box I used: 64mm x 50mm x 44mm with roughly 8mm leeway when adding the top. I probably could have used a smaller box, but it's especially difficult to cram everything in there when including batteries and a holder. So, your mileage may vary.
The first step should be to take the board, Arduino, headers (maybe affix them with some Scotch tape), display, module, and whatever battery you will use (if any), and see if you can jam them in the box you want to use. Remember, there will also be some wires which can get in the way, so leave a little room for fudging.
In order to access A4 and A5 of the Arduino, you will need to solder two (2) headers onto the board (at least on my version). I used male right-angle headers to save space.
To Be Cont'd