you could use one of the golden ratio's if you wanted.
cube root of the needed gross internal volume is the first side in feet(internal size) then multiply that number by 1.2599 to get the second side, then multiply the first side by .7937 to get the third internal measurement. Supposedly it supposed to be optimal for eliminating standing waves, which will help impedance as well as tansient response.
If you want to know the needed gross volume just use the woofers recomended net sealed volume spec plus its displacement.
If you use screws screw every 4 inches and predrill. Use a quality wood glue. As long as your cuts are straight you won't need caulk, but it won't hurt..
I use screws in almost every box... i've ripped box's with the screws removed and the glue didn't hold worth a sh!t. It just flaked off the top layer of mdf.