Just to add my experiences to the list: I worked a lot with my first two greyhounds and they both learned sit, down, come, stay, twirl (turn around on rug when coming in from outside to help reduce muddy pawprints), move, out (of the kitchen or dining room), left (walk on my left), and different walk speeds, for when I was jogging or if it was okay to just mosey. I've probably forgotten some other cues.
I've gotten lazy with the more recent dogs, but everybody still knows come, down, stay, move, left, and out. They know not to jump up on people. Everybody has learned to accept nail cutting and ear cleaning. All have learned to use the dog door, except Scout, who refused to go out the door. Everybody knows not to counter surf right in front of me, although I've never been successful in completely banning it.
I use almost all positive reinforcement. Eve, my first grey, also needed neck-scruffing on a very few occasions(recommended by Kathleen Gilley of the Dancing Greyhounds fame -- no physical harm, just a reminder of who's boss) to reinforce acceptance of nail trimming and no counter surfing. Scout could also be extremely stubborn, but the other three have been eager to please. I should be doing more work with Romie -- he's very smart, learns from just one "no," and would probably enjoy more attention and work.
Most retired racing greys come with some basic manners, and it's easy to expand on that. You'll enjoy working with your greyhound and having the best behaved dog around.