They are super dogs, and you can get one from smallish to huge, in just about any color, and from as young as 18 months to as old as you prefer (I prefer old). They love their lives on the farm, growing up, then racing, and are well adjusted and love people, though like any breed, some may be shy or timid, most are not.
Adoption depends on the group or kennel. My group is very easy going and a pleasure to work with. We will work with you if you have cats, small kids, no fenced yard, etc. Some dogs need a fence, but many do not. Some groups are too strict I think, but if you don't like one, just look for another. Usually you apply, meet some hounds, get a home visit (nothing invasive!). Then they will show you some dogs that they think would match your lifestyle, and you select the one that you feel connected with.
Some groups have a kennel, and like a shelter, you just go meet them and adopt the one you like. Other people simply get their dogs directly from a racing owner or kennel, though you need to know someone in the business to do that, but it's possible to even "preadopt" a dog still racing, follow its career, then bring it home! That can be a lot of fun, too!
Most Greyhounds are fostered in a home, so they are housebroken, know basic manners, and adjust just fine. But even a dog right off the track seems to fit right in most of the time. Due to their careers, they are already leash trained, kennel trained, and used to other dogs, but some will chase small fluffy dogs and cats- but many live just fine with small pets (most, probably).
If you want some info about Greys in your area, just let me know where you are!