Consider shampoo/flea treat immediately, ideally before they get in the house. Keep an eye on their poo and be prepared to get worming tabs from the vet if it starts waving at you 🤮
I've had more than one dog come from racing kennels with "passengers"!
Keep them on a short lead with treats in your pockets for a couple of days and any time you think they might need to go, take them out pronto and praise and treat any "performance" outside!
Oh and get Simple solution for if there are slip ups. It's ok to sound alarmed and disappointed ("nooooooo!") as you rapidly haul them (still peeing no doubt) out the back door, but being angry or mean is counter productive, they are sensitive little souls.
Immediately establish your right to turf them off the sofa, bed etc. You'll be unlikely to keep them off but you do want to be able to move them if needed!
Routine routine routine, they're used to having one, they just need to know yours.
Keep things nice and calm and let them have their quiet time so they can settle.
Get insurance sorted right away!
Start on teeth brushing soon, greyhounds have terrible teeth often! I find an electric toothbrush with just water is easiest as you just have to move the lips away from teeth and gums and place the brush on.
Do fasten the collar as tight as they tell you and don't get an extending lead or let them off the lead. Losing a dog or a finger is bad!
Lastly bear in mind that previously, any food they saw being prepared was for them.... Oh and they may not know about stairs. Worse still they may work out "up" several days before "down" 😎
Good luck, they're great! Big hearts. Kind of odd compared to "normal" dogs but I've had them for decades and love 'em. Don't be too upset if they fail to fetch, sit, or ever recognise a word you say, they have good emotional intelligence and can be negotiated with quite well, they mean well even if they're not great intellectuals !