Want to type you a lovely long answer, but have a banging migrane, so will give you a low down instead.
IG - Wouldn't have with very young children, are quite fragile and don't tend to like much hurley burley, can be very hard to house break, tend to cost £££££.
Whippet - Great family pet, nice size, usually good with animals they are brought up with,l though just because they love and happily sleep with your own cats they may try to get any they see 'off territory', they can do 35mph so need excellent recall training, cheap to feed, need approx 1-2 hours walking a day (but can walk for much longer) some excercise must be free running, you will need a garden that is securely fenced to six foot minimum, very loving, very loyal, cannot be kept off the furniture.
Greyhound - As above but bigger, and a bit more lazy and laid back, still very loving with children but probably less inclined to play, as mentioned unlikely to get a puppy, so really looking at a rescue, you may have to wait for one that is cat friendy, but the do come up fairly often.
For any more advice can I direct you to The Whippet Forum for advice on all things sighthound related .
Actually that was quite a long answer, please ask if there was anything else, or ask/search on the forum.