We had a greyhound who sadly had to be put to sleep in 2003. She was a reject and I can understand why. She showed no inclination whatsoever to chase anything except squirrels - why squirrels held such a fascination I will never know.
Butterfingers, it's interesting that your dog wasn't house trained. Our girl was and I'm told that most are very quick to house train if they're not already.
Greyhounds like their comfort - a duvet, a settee, a double bed - and they can be quite lazy as well. Also, mine hardly ever barked. Neither would she sit or do anything in the way of obedience, and she had no traffic sense, either, so make sure your garden is secure. Also, some of them can jump quite high, so check your fence heights.
As Butterfingers says, they are the most loving, gentle and affectionate dogs, quiet and clean around the house (usually) and a joy to have around.
Good luck.