The answer depends on how you construct the box and the thickness of the material you are using. Start with the outside dimensions & decide 1st how you want to join them. The simplest approach is butt joints with the sides overlapping the ends of the front/back/top/bottom. In this case the sides are cut full size, the front & back are full height and width is full width minus 2x thickness, and the top & bottom are full width minus 2x thickness and full depth minus 2x thickness. If I were using this approach I would reinforce all of the joints with biscuits. If you decide to use rabbets in construction it gets more complex as the depth of the rabbet is also a factor. The bottom line is that you should always draw what you are going to build (preferably full scale) before you build it. It is much easier to catch and fix mistakes made with a pencil (eraser works well) that those made with wood!
One other thing...most wood suppliers are happy to rough cut (+ 1/16" or 2mm) your wood down to make it easy to transport but if you want it cut to finished dimensions (+ 1/64" or 0.4mm) you should expect to pay per cut. I would also size the sides (if those are to the full dimension) a bit generous (maybe +1/64" or 0.4mm) so that you can assemble the box with a slight overlap then use a flush trim router bit or sander to bring them flush to the mating parts.
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