An accent chair is the one seat in the room that doesn't have to agree with anything else. It gives you somewhere to sit that isn't the sofa, and it does the job of pulling a corner together that would otherwise just sit there empty, a lamp and a plant with nothing to talk to.
These work hardest in living rooms and bedrooms, the spot by a window where you actually read, or that awkward nook off the kitchen that needs a reason to exist. They suit older houses with a bit of character just as well as a plain rental, maybe more, because a good chair can carry a room that has nothing else going on architecturally. Cold months are when you notice whether one earns its spot, when you're sitting in it for an hour with a book and a blanket rather than passing through. When you're shopping or unpacking a delivery, sit in it properly, not a quick perch, and check the arm height against where your elbow actually falls, check the seat depth against your own thigh length, not some average person's, and look at how the fabric is attached at the welting and seams, because that's where cheap ones start to pull first. Give the frame a shake. If it wobbles in the shop, it will wobble worse at home.
Fabric matters more over time than it does on day one. A tight weave or a performance fabric will shrug off coffee, red wine, a muddy paw print, wipe it, let it dry, move on. A loose linen looks wonderful in a photo and shows every mark within a month, and cushions on a well loved chair will need plumping and occasionally refilling after a year or two of actual use, which is normal and not a sign you bought the wrong thing. Wood legs scuff during a move, so wrap them, and a chair that's shifted houses twice with no tightened screws is a chair that will start creaking on you.
For size, measure the space with the chair pulled out to where you'd actually sit in it, not pushed against the wall, allow at least a foot of walking room on at least one side, and bring a tape measure to the doorway and stairwell before you buy, because an accent chair with a fixed frame and a wide arm can get stuck in a hallway turn in ways a flat pack sofa never will. The biggest mistake is buying one too large for the corner because it looked small in a showroom. It won't look small at home.
I'd put the first one by a bedroom window, where the morning light is good and nobody else has a claim on it.