I'd be most concerned about any box that uses glue. The clear plastic in window boxes call fall out. Any box that, how shall we say, wraps around and glues to itself can be a problem, too. I wouldn't be as worried about clamshell boxes, as long as they're not in a really humid environment.

Those large plastic tubs may sound nice, but not hold as many boxes as you think, given that the stuff you're putting into them isn't malleable. Lots of empty space left over, unless you were really good at Tetris as a kid.

I'd get really big plastic bags , line the big cardboard boxes, put your boxes in there, seal the bag, close the big box.