What of the cheapest moving boxes?

Well, those boxes sold in stores and moving rental companies may have the ratings; but are usually not the least expensive in the long run. Some places are also recycling moving boxes and you may have some stashed away from the last time. That is well and good if you know they will go on the top of the pile, have not been exposed to the elements (snow, rain, extremes in temperature), and the approximate age. Those seams at the edge of the packing box can easily split as they age, have been stressed, and handled. You should reinforce those seams with a good quality packing tape on all four corners; just to be sure. Use the storage box for lighter items and pack them snug but not tight: tight will cause additional stress on the walls and the tape may not be sufficient to preserve the integrity of the shipping box.

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