The moment this clicked for me was pulling winter sweaters down from a closet shelf without a chair or a step stool. A box with cutout handles, or proper rope or leather ones fixed to the sides, comes down with one hand while the other holds your coffee. Anything you store up high or shove under a bed only earns its spot if you can actually get it back out again, and that is the whole case for handles right there.
When you are looking at one in person, or opening the delivery box it arrived in, check how the handle is actually attached. Stitched or bolted through reinforced fabric or a wood frame will outlast you. Handles that are just glued onto cardboard or thin plastic will tear off within a year, usually right when the box is full and you are lifting it over a closet door track. Press on the base too. A box that bows or dents under moderate weight is going to sag permanently once it has books or winter boots in it for a few months. Lids matter as well, you want one that sits down flush rather than perching on top, because a crooked lid means dust gets in and the box never quite closes right again.
On finish, plain neutrals age the best, not because color is wrong but because a box you see every day on an open shelf needs to disappear a little. Natural canvas, soft gray, a muted rust or a deep green all go quiet after the first week, where a bright print or a bold geometric pattern starts to feel busy fast, especially if you end up buying more of them later and they do not quite match. Woven rattan or seagrass with leather handles is the one finish I have genuinely not gotten tired of, it goes in a nursery, a home office or a mudroom without looking like it belongs to any one of them specifically.
If you own none of these yet, start with one mid sized lidded box in a neutral fabric or woven finish, something that can hold either folded throws on a shelf or loose cables and chargers in a closet, since that flexibility is what you will actually use in the first few months while you figure out where storage is genuinely short in your home. A box that has moved apartments twice and still has handles attached and a lid that shuts flat has earned its keep, full stop. Measure the shelf or cubby depth before you buy, since a box that is an inch too deep will stick out and catch on everything every single day.