Before you buy a single one, figure out what shelf or closet it needs to live on, and measure that space, not the box. I have carried home plastic bins that seemed perfectly reasonable in the aisle and then watched them refuse to fit under a bed by about half an inch, which is its own special kind of defeat. Get the dimensions of the gap first, height included, because a lid that needs an extra two inches of clearance to lift off will make you take the whole bin out into the hallway every single time, and you will not do that more than twice before you give up.
These do not age the way wood or metal does, there is no patina coming for a storage box, but they do wear, and how they wear tells you everything about whether you bought the good one or the cheap one. A decent box keeps its shape after a winter in a garage or an attic that gets properly hot in summer, the plastic staying rigid instead of going soft and bowing at the sides. A bad one goes brittle at the corners within a year or two, and you find out when a lid snaps clean off in your hand while you are holding a box of Christmas ornaments over your own head, which happened to me once and taught me to stop buying the cheapest option on the shelf just because it was the cheapest option on the shelf. Keep them out of direct sun if you can, since UV is what actually breaks plastic down over time, and wipe them out before storing anything fabric, because trapped moisture in a sealed box is how you end up with a smell that no amount of baking soda fixes.
The difference between a box that lasts and one that does not usually comes down to wall thickness and the hinges, if it has them. Pick one up empty and flex the side with your hand, if it feels thin and flimsy empty it will feel worse once loaded with books. Check that the lid actually seats into a lip all the way around rather than just resting on top, that lip is what keeps dust and mice out, and it matters more in a basement than you would think. On delivery day, check the latches open and close without needing both hands and a bad mood, and stack a couple to be sure they nest or stack cleanly, since a box that only balances at an angle is a box you will eventually trip over.
So before I put one in the cart, I ask myself: will this still be doing its job in five years, or am I buying next year's broken lid right now?