The thing nobody tells you until you have ruined a floor is that the backing matters more than the pattern on top. A rug that looks wonderful in a photograph can still slide across floorboards the moment someone walks fast through the room, or it can be so thin that every chair leg eventually punches a dent straight through to the wood. Before you fall for a color or a weave, ask what is underneath it, because that is the part doing the actual work.
A well made rug has some heft to it, enough that it sits flat on its own rather than curling at the corners like a bad toupee, and the pile feels dense under your palm rather than hollow. Natural fibers like wool take a dye better and spring back after furniture presses into them for years, where a lot of synthetic blends stay flattened once something heavy has lived on them a while. Run your hand along the edge and feel for a bound or serged finish rather than a cut edge that will fray the first time it meets a vacuum, and check the knots or tufting on the back, because a rug that was made properly will look almost as tidy underneath as it does on top. I learned this the hard way with a jute runner in the hallway that looked rustic for exactly one winter before it shed itself into a small haystack by the front door.
Where a rug lives changes what it needs to be. A thick, soft rug earns its keep in a bedroom or a living room where bare feet and lounging happen, something you sink into rather than just stand on. Kitchens, mudrooms and anywhere wet boots or dog paws pass through want something flatter, washable or at least forgiving of a sponge and some patience, and a good non slip layer underneath is not optional if there are small children or anyone less steady on their feet moving through that space. Smaller mats by doors and sinks take the worst daily abuse of all, so that is where I spend the least on sentiment and the most on grip.
The day it arrives, unroll it somewhere you can actually walk on it rather than just look at it, because rugs photograph flat and lie flat differently once there is foot traffic and furniture weight involved. Check that the edges lie down within a day or two rather than staying curled, listen for whether a dropped object sounds like it landed on something or just skidded across it, and make sure any rug pad you are using is the right thickness for the floor, not just whatever was on sale.
A good rug suits a home where people actually live on the floor, not just admire it from the doorway.