Small chests used to mean one thing in a bedroom: the orphaned piece next to a bed that was too narrow for anything else to fit. That has shifted, and for the better. People now put them in entryways, bathrooms, kitchen corners, anywhere a few drawers would solve a problem without taking over the room, and furniture makers have caught up with that use rather than treating the small chest as a leftover scaled down version of a real dresser.
Wood settles into these over time the way it does with any piece built to be opened and closed for years, so look for solid drawer boxes, not thin stapled sides, and runners that are either wood on wood or a metal glide with some weight to it, because the cheap plastic ones wear a groove and start to stick within a couple of years no matter how gently you use them. Dovetailed corners on the drawers tell you something real about how it was made, you can run a finger over them in the shop and feel whether they were cut or just glued and pinned. On delivery day, pull every drawer all the way out, check that the chest sits flat on the floor without a wobble, and look at the back panel, a thin stapled sheet of fiberboard is fine for keeping dust out but it should never be the only thing holding the frame square. Wax or oil a solid wood top once or twice a year, keep it out of direct sun if you want the color to stay even, and wipe up water before it sits long enough to leave a ring. In a room with other furniture, a small chest reads best against a plain wall with nothing else stacked beside it, a lamp or a small mirror above does more good than a second piece of furniture crowding its other side, and in a narrow hallway or a bedroom with a low ceiling, four drawers at waist height leaves far more breathing room than people expect from something that size.
The difference between one that lasts and one that loosens up within a year comes down to the joints and the hardware more than the finish. A solid wood frame with proper joinery will take knocks and still close square, while a piece built from particleboard with a veneer skin tends to swell at the first sign of damp and never quite recovers. Handles matter too, solid metal pulls with a real weight to them age well and can be swapped later if your taste changes, where thin stamped metal starts to look tired fast.
For a first one, I would put it in a bedroom, right where a bedside table usually goes.