I'll have to chime in on the greyhound, too. We have one that was a racer and she is the sweetest thing. She's great around my kids and she thinks DH hung the moon or something. She's so funny, she'll walk up to him and twist her body around his legs so he can't leave until he loves on her ... for a long time.
We have cats, too, so when we got her, we did watch very carefully to be sure she didn't try to eat my cats. One was not even 6 months old yet. Lady got used to the cats and now the cuddle on her bed.
Love, love, love greyhounds. She is our second one, too.
Hope you give them a thought.