The first thing I do is open the lid and smell it. Cheap wooden storage has that flat, slightly chemical smell from the finish, and it never really goes away. A well made box smells like wood, maybe a little like the oil or wax they used on it. If a box smells like a craft store on day one, it's going to smell like that for years on your landing.
On color, I've learned to stop fighting the wood. A natural or light oak finish goes with almost anything you add to a room later, which matters when you're furnishing one room at a time and don't know yet what the rest of the house will look like. Painted boxes in white or a soft sage look great on day one and then date fast, or chip at the corners within a year of normal use. Dark stained wood, walnut or a deep mahogany tone, is gorgeous but shows every scuff and water ring, so it's a better pick for a bedroom than an entryway where wet boots are landing on it. As for build quality, pick it up and check the corners first. Good ones are joined, dovetailed or at least properly screwed and glued, not just stapled or nailed through thin panels. Give it a gentle twist, a well built box barely moves. A cheap one flexes in your hands like a cereal box. Check the lid too, it should sit flush and close with some resistance, not just flop down. Solid wood or a real plywood will have some weight to it. If a storage box feels suspiciously light for its size, it's probably held together with the wooden equivalent of hope.
Measuring matters more than people think, because wooden storage doesn't flex the way a basket does once you've misjudged the space. I measure the exact spot first, then take off a couple of inches on each side for breathing room, because a box that's a tight fit looks jammed in rather than placed. Height matters too, a box under a window needs to sit below the sill, and one doubling as a seat or side table needs to be close to typical seat or table height or it'll feel wrong every time you use it. The common mistake is buying one box for a job that needs two smaller ones, which ends up heavier to move and less flexible if you rearrange later. I'd rather have two boxes I can shift around than one big one that becomes a permanent fixture whether I like where it sits or not.
Would I actually use this every single day, or am I just buying it because it looks nice empty in the shop?