A friend, David asked how thick I make my box sides and how thick of lumber I use to obtain the desired thickness.
There are no exact formulas for how thick box sides should be. There are a number of considerations, including your choice of hinges, and the overall size. Obviously smaller boxes require thinner sidewalls to have a reasonable proportion between inside and outside space.
In terms of thickness, for most of my boxes, particularly for those using resawn material for the sides, I use full inch stock which tends to run a bit on the thick side, about an inch or an inch and a sixteenth. Or for fans of the metric system, between 2.54-2.88 CM. Fifteen sixteenths inch (15/16") stock will usually provide box sides in the 5/16" to 3/8" range. If the stock is full inch or slightly more, I can sometimes get 7/16" stock from it if it is straight. I rarely have 5/4 stock to work with as it is hard to get unless I have it milled myself, but it is my wood of choice when I need box sides as thick as 1/2". All said and done, I don't worry too much about exact thicknesses, just that all that I'm using is the same.
I get these same results whether using a thin kerf blade on the table saw, or with my band saw when it is well tuned.
I am pleased to hear that David is enjoying Box Making 101.