We've had our retired greyhound for about 3 years now and love him so much!
No kids yet so can't attest to how they are with kids in the home, but he is always very gentle and good natured with kids that come up to him out and about, although they do get a bit startled sometimes when he swings his big nose around to have a sniff 😁
They are super chilled, lovely, low maintenance pets. Ours had impeccable manners with other dogs from the off. Very low exercise demands, our boy does really enjoy his walks but they're more about sniffing and reading the pee-mails than striding out and covering ground. You will not get your heart rate up by walking a greyhound lol.
It's worth splashing out on a good quality wet food if you can, as their tummies are sensitive and you will know about it if they're not happy 😅
Ours froze a lot on walks when we first had him. For us this was something that mainly improved with time. If I could do it again I wouldn't worry about venturing too far from the house in the first weeks. They need time and patience to get used to the sights and sounds of the outside world.
Watch out for space guarding when they're sleepy/asleep, e.g. don't plonk down next to them on the sofa when they're dozing or stick your face into their bed. This is the only thing they can be a bit funny about. If they grumble just give them space, don't be alarmed, they're just communicating. They are not aggressive dogs at all.
Good luck! They are quirky, beautiful souls and ours brings sunshine into our life every day. :)