"But some greyhounds, as with any breed, have VERY HIGH prey drive. Dont get me wrong, I love em. Just make sure you socialize the crap out of whatever puppy(or rescue) you do go with and throw in some obediance classes.Some goldens tend to be as hyper as any labs. Again, great breed, but I've seen just as many silly goldens as I have seen calm ones. "..

Its not a "prey drive" its a "chase drive". When you think about it, if they will chase a white plastic bag, they will chase anything. They are also naturally great with people- as they perceive themselves as one. They do great with strangers, and naturally accept people. They also make excellent therapy dogs as well.
These breeds are not like a shepherd, dobie etc. They are natural people dogs. They do not need high socializing as they are already accepting. They do have a royal pressence about them, and can ignore strangers. With Borzois its like " do not mess up my coat with your dirty hands.. lol. " However accept in a calm pressence.
As far as accepting cats- depends on the dogs. There are some precautions you can do. Remember- they may accept the cat in the house, however- turned loose in the yard with a fleeing cat could court disaster. Hottie was raised with a papillion, and one maine coon ( the cat died when he was about 6 months old I guess from urinary cancer.) Anyway- the papillion- when I had them in the yard- one of them was leashed. Or turned out seperately - other than that my papillion ran the house. They are so aware of their feet, I was never worried about my papillion being stepped on either.