People find a vintage rug they love and buy it the way they'd buy a new one, matching it to the sofa, the cushions, the lamp, everything color coordinated down to the last thread. Then it sits there looking like it's trying too hard, which is the opposite of what these rugs are supposed to do.
A worn, faded rug with some age on it does not want to be the only thing in the room with a personality. It clashes hardest with furniture that's already loud, a bold patterned sofa, busy curtains, a feature wall in some color with a name like "Amazonian Dusk." Put a vintage rug in a room like that and everything starts competing for attention and nothing wins. These rugs work best as the one thing in the room that's doing something interesting, with everything else around it kept fairly plain and happy to let the rug get on with it. For color, I'd steer toward the washed out reds, the faded blues, the soft rust and camel tones that look like they've had the sun on them for a few decades, because those shades sit calmly with almost any wall color and any wood tone, pale floors, dark floors, doesn't matter. Avoid anything with a lot of bright, saturated color still intact, those are harder to live with long term even though they're the ones that grab you in a shop.
For sizing, measure the room first, not the rug. In a living room you want the front legs of your sofa and chairs sitting on the rug, not floating off the edge of it, which is the single most common mistake I see, a rug too small marooned in the middle of the floor like a bath mat. Measure the full seating area and leave a foot or so of bare floor around the edge if you can. Vintage rugs are often slightly irregular, a few inches off square, sides that aren't quite parallel, and that is normal and part of the charm, not a flaw to worry about, so don't measure them like you would a new one and expect factory precision.
If you've never owned one, start with something small and low pile, a runner for a hallway or a kitchen, where the wear and the unevenness won't bother you and you'll get a feel for how good worn wool feels underfoot, soft in a way new rugs rarely are, and how satisfying it sounds when something gets set down on it, a quiet thud instead of a hollow clack on bare floor.
I'd put the first one in the living room, under the coffee table, where you'll actually feel it under your feet every day.