The first thing I check is the bottom. Press it, flex it, see if it bows under its own weight before anything is even in it. A box or basket that feels flimsy empty is going to feel a lot worse once it's holding sweaters or tools or whatever has been living on the floor for a year.
If you own none of this yet, start with a set of plain lidded boxes in one size before you buy anything with a specific job in mind, like garage bins or jars for the pantry. One size, stacked, is more useful than five mismatched ones, because you can move a whole stack as one unit when you need to clean behind it or when you're packing up a room. Baskets are the second thing to add, mainly for stuff that gets used daily and needs to be grabbed without opening a lid, blankets, mail, the charger cables nobody can ever find.
The gap between a good one and a bad one shows up fast. Cheap plastic boxes flex at the corners, the lids don't sit flush, and after a few months in a garage or attic they go brittle and crack right where the handle cutout is, usually while you're holding it over your foot. A well made box has a lid that seats properly without forcing, a bottom that doesn't dish in the middle, and if it's got handles, they're reinforced, not just a hole punched in thin plastic. With baskets, look at how the material is finished at the rim and the base. Woven ones should have the ends tucked and secured, not just trimmed, or they'll fray and shed fibers onto the floor within a season. Metal storage lives or dies on the welds and the coating, a rough seam or a thin coat of paint will rust the first time it sits somewhere even slightly damp. Clear boxes show every flaw, so any cloudiness, warping, or seam lines mean it won't hold up to being hauled around.
In an ordinary room, these sit well under console tables, on closet shelves, stacked in a mudroom corner, or tucked under a bed where nobody but you knows they're there. Open shelving looks calmer with a few matching boxes on it instead of loose stuff. A basket by the door for shoes does more for a hallway than almost anything else you could put there.
The one mistake is buying based on looks alone and skipping the lid test. A beautiful box with a lid that pops off when you lift it is just a shape you'll be annoyed at twice a week.