My best piece of advice for greyhounds is to never underestimate them. Mine played the angel until he had his feet under the table. Now he's a little monkey despite being 9.5 yrs old. They'll play the fool, and then go and surprise you by eating a whole Guinea fowl off the worktop, or eating the pocket off your new waterproof just because it smelled of biscuits.
We consider our dogto be bottom of the pile for brains. Google 'Wesley the naughty greyhound' for how we learned one of many lessons.
I guess the rescue have told you about wide collars, raised food bowls, and the need for coats? My very fine coated lurcher (is v similar to a grey) needs his fleece housecoat on all the time now, and a coat outside. Milgi coats are brilliant, and I buy leads and collars from Meggie Moo.
We've had greys for nearly a decade and our resident criminal mastermind snaffled my margarita pizza this week when I'd turned my back for a second. They have a reach and speed that is impressive when it comes to food thieving.
One of the reasons they are often described as not having much brains is that unlike "pet" dogs, they don't receive much early training in responding to cues. So something like a spaniel pup will be learning cues like Sit, stay etc from the word go, whereas a grey will never have experienced it, and is learning from scratch, and therefore understandably take a lot longer to learn things. Having said that, they can and do enjoy training immensely - I've taken an elderly grey to KC Gold level and am doing Rally with one of ours at the moment. I know greys who do agility and plenty who do basic obedience training.
The other wonderful thing about greys is the amazing social life that comes with them. It's actually more like joining a cult - you'll soon find it's impossible not to talk to other greys when you meet them, and all greyhound rescues have a thriving social scene of walks, playdates, etc. We've been crisscrossing the country recently for various hound related festive get-togethers - it's wonderful. It's also virtually impossible to stop at one - greys thrive as part of a multi dog household since that is how they were raised and trained. Again, unlike pet dogs, they have spent their whole lives being with other greys which is why they enjoy their social get togethers so much.
And being able to sit on your own sofa will quickly become a distant memory....