Mrs tandemwarriors had always had dogs, but I never had. Our first was a rescue greyhound, and he was just brilliant. They're so used to being poked and prodded at the track that a toddler climbing all over them and under them is barely worth waking up for! Red would have a 20 min walk morning and night, but would happily go longer if offered. If it was raining (pretty likely here in Argyll), he'd look out the door, look at me as if to say "aye, right", then go back to bed. They are the most regal looking dog, and those eyes just make you melt inside.
Only thing to be careful of, and any good greyhound re-homing charity will spell this out over and over again, is that they have been bred and trained to chase anything small and furry. So cats, small dogs, rabbits, squirrels, are all perfectly reasonable prey, so having them running off the lead can be difficult until you've got a good recall trained into them. Daughter-tandemwarriors has a ex-racer with good recall so happily runs off the lead.
Here's Red at full speed in a local field, just a beautiful sight...

Most greyhound charities have open days where you can meet the dogs and they'll see if you're an appropriate home for an ex-racer, go have a look, you won't regret it.
Rob