I own a rescued racing greyhound that I adopted.
First, because of the relationships that they have to maintain with the trainers, the rescue groups are racing neutral so don’t go bad mouthing racing in front of the rescue group.
Second, the dogs are like aliens when they come off the track. They have never been in a car (don’t know how to jump in the backseat), never been on stairs, never seen a glass door (ours walked right into one right after we first got him). Most especially, they are not used to large spaces (back yards and neighborhoods). All of that will take some adjustment. It might help your dog to sleep in a crate when you first get him or her.
They are very loving to people, but have not been exposed much to children. I would never leave a greyhound alone in a room with a baby.
The rescue groups do not tell you that approximately 40% of the dogs never lose their high prey drive. This means they cannot be around cats or small dogs. (or rodents) They will kill them. This is true of our dog sadly.
You will be richly rewarded if you adopt one. They can be very funny and real characters. They are truly affectionate.
If you have any questions, you can PM me.