Hi cranberry15, I have adopted three retired racers and think they are wonderful! My suggestion is that you read all that you can --"retired racing greyhounds for dummies" is a 'greyt' book!. Then contact an adoption agency near you and talk to them about your situation. They will be the experts that can give you all the info that you need.
gg

(ps-I am just a lurker here but had to come out to comment on your post. :))

First they will be neutered , they have to be taught to climb stairs. They are adults they may attack a child in diapers or small animals because they have been trained to follow the mechanical rabbit.

I had a three year old in the house at the time of my first adoption and although she (the dog) was terrified of her, there were no problems because as with any animal we were careful and never had the dog alone with her (which I'm sure, would be what any responsible person would do with any animal).
We now have a baby in the house (11 months old now) and although the dogs are curious about her, they show no signs of attacking her. Of course we are still being responsible about it and not leaving the dogs and the baby alone together, but we would do that no matter what kind of dogs they were. :)
Our dogs are extremely laid back and gentle, but they are animals and are treated with the caution that they should be.
When they come from the track they are entering a world that is totally foreign to them. They have lived in a cage and have never been in a house with all the things that we don't even think about....stairs being one of them. They are very intelligent and learn very quickly. The gratitude that they show for the love that they experience for the first time in most of their lives is so worth it! Adopting a greyhound is not like adopting a 'regular' dog. They do have different needs and requirements, but they are very worth the little effort it takes to learn about what those needs are.
***they make wonderful pets*** :)
gg (who hopes that this post sounds like it was intended.....just informative about what my experience has been :))

They have advantages: the lowest hip diplasia of all large dogs (98%hip diplasia free), quickest reflexes , good eyesight , fastest runners over short distances . I think the red brindle is the prettiest . they will still have to be house broken as they have always lived in a kennel .

Greyhounds are the highest jumpers of all dogs able to clear a hurdle of over 5 feet . At least they will keep the jack rabbit population down . Let us know how you make out . They are worth having if you have a use for them . You also get a copy of his racing record ; and sometimes his racing colors . I would pick a fast one . good luck !