Oh wow! How exciting and what a fantastic choice of breed. And thank you for rescuing an ex racer! Greyhounds and lurchers are my absolute favourites (as you can see from my user name!) and great dogs for less experienced owners. They tend to be friendly, chill and very low maintenance.
However, there are some complications from the fact that you are taking on a dog who has previously lived in kennels, so do find out as much as you can from the rescue you are rehoming from. Things that spring to mind are:
- has he lived in a house before? He may not be house trained. Even if not don't panic. Many seem to house train themselves, pretty much, very quickly. If not you can find loads of info on line about house training an adult dog, but it may impact your choices about where he sleeps to begin with, etc.
-chase instinct is just massive with these dogs. Do you have any other pets? Do family members you would visit? Do cats currently come into your garden? All things to think about. Some ex racers can be fine with cats, but it's by no means a given. They also need to be watched around very small dogs. If you walk him in a place where small dogs are off the lead, even if yours isn't, please be careful. Until you know him well, maybe avoid very "doggy" areas/warn other owners that he is new and to keep their small dogs away.
-recall - many owners can't ever walk them safely off the lead because they just don't come back (some are fine of course). Luckily they don't need huge amounts of exercise compared to some other dogs, but they do need the chance to have a quick zoom every day - is there a secure dog field you can take him to?
-sleep startle - my friend accidentally woke his beautiful greyhound by leaving over him and needed stitches on the face! Not the dog's intention or fault - when they are woken suddenly there are a few seconds where they literally don't know what they are doing. Please warn your kids to be very very careful when the dog is sleeping, and any visiting kids need supervising (but that's true with any dog).
Last thing I would say is they are all different - I have talked about common greyhound/lurcher traits, but some recent research apparently suggests dog personalities may be less fixed by breed than we sometimes think they are. So find out as much as you can about him, and if you find anything unexpected happening, do reach out for support, on here or to the rescue you are using.
And enjoy! They truly are the best boys and girls ever - at one terrible point in my life when I was very very low my friend's greyhound sat for hours with me on the side with his head on my shoulder, and I believe literally played a big part in saving my life!