Will gray chairs look cold and showroom like in a normal room? Only if the gray is too cool and everything else around it is cool too. Pick a warmer gray, the kind with a little brown or green in it rather than blue, and it reads as neutral furniture, not a design statement.
Gray sits well next to almost anything because it isn't really a color decision, it's a volume knob. It turns down next to warm wood tones, a honey oak table or a walnut sideboard, and lets those pieces do the talking. It turns up a bit next to white walls and natural light, especially in the morning when the room is brightest, and it goes a little moodier and more interesting in the evening under lamp light, which is when most gray upholstery actually looks its best. Pair it with warm metals, brass or bronze, rather than chrome, and with at least one other soft texture in the room, a wool throw or a linen cushion, so the whole thing doesn't start to feel like a hotel lobby. The mistake I see most is matching gray chairs to a gray sofa and a gray rug and calling it a scheme. It isn't a scheme, it's a fog bank.
On sizing, measure the actual floor space you have around the table or the seating area, not just the chair itself, because gray chairs tend to get bought for dining sets and small gaps show up fast. You want at least two feet of clearance behind each chair for someone to push back and stand, and if you're buying a pair for a living room, measure the width across both chairs plus the side table or gap between them before you commit, because two chairs that looked modest online can eat a surprising amount of wall. The other mistake is buying scale for the room rather than the person sitting in it. A deep, low gray armchair looks right in a big living room and swallows anyone under five foot six in a smaller one.
If you own zero gray chairs right now, start with a simple upholstered dining chair in a mid tone gray, something with exposed wood legs rather than fully upholstered down to the floor. It's the easiest one to place, the easiest to clean, and the easiest to add a second pair to later without them fighting with whatever gray you chose the first time.
The detail I actually look for now is a removable, washable cushion cover, because gray shows every coffee ring and crumb a shade darker than any other color does, and a chair you can strip and wash in ten minutes is a chair you'll still like in three years.