Chests get called the practical cousin of the dresser, the tall narrow one you put in a spare room because it fits where nothing else does, and I think that reputation undersells them. A good chest is just a dresser that went to the gym instead of the buffet, same storage, smaller footprint, and in a lot of real bedrooms that trade is worth making. The catch is that because people treat them as an afterthought, the construction often is too, so this is one where checking before you buy actually pays off.
Pull a drawer all the way out before anything else. You want to see how it's joined at the front corners, dovetails or at least a solid interlocking joint, not three staples and a prayer, and you want to feel the runner glide rather than scrape or rock side to side. Flip the whole thing around if the shop lets you and look at the back panel. A thin stapled sheet of hardboard means the chest will rack and lean within a year or two of real use. A panel screwed into a proper frame means it'll still be square when you move it into your third apartment. Over time a chest earns its keep or doesn't based entirely on those runners and that back panel, since the top gets a lamp and a tray and not much else, it's the drawers doing all the daily work. Solid wood ones will take decades of opening and closing if you keep them out of direct sun and wipe spills promptly, and a light coat of furniture wax once a year keeps the wood from drying and the drawers from sticking. Veneered ones need you to be more careful about moisture right at the edges, where the veneer lifts first.
On color, I'd steer toward a natural wood tone or a simple painted white or soft gray over anything trendy, because a chest sits in your eyeline for years and a loud finish gets tiring fast, while a plain one quietly matches whatever bed or rug comes next. Where it struggles is in a small bedroom with a low ceiling, since the height that makes it space efficient on the floor also makes it loom, and in a room with an already tall wardrobe or bookcase nearby, where two tall pieces competing for the same wall just reads as clutter.
What a chest won't give you is wide, flat storage for folded sweaters or bulky linens, the drawers are narrower and deeper by design, so if that's your main need, a wider dresser will serve you better no matter how well the chest is built.