I just adopted a ten year old broodie (former Mama of racers) and she is awesome, and I have had so many Greyhound fosters I can't count them all anymore. I did the adoptions quite successfully, matching dogs (which I knew from the racing kennel) into good pet homes.
I have worked at a professional racing kennel feeding, walking, exercising, and caring for the dogs, and I am obsessed with all things sighthound!
All that said, my experience is that these are AWESOME, easy care dogs. They can absolutely live happily in an apartment, probably better than most breeds. CERTAIN Greyhounds do need a yard, but many do not. They naturally walk well on leash thanks to their racing days. They usually only pull on the way to the race since they LOVE to race so much!!! They are NOT abused (and don't argue this if you haven't worked at a dog track and handled hundreds of racers like I have) and they get loving and cookies and have nicknames and we get to know their quirks and habits. It's the most fun job in the world!
Most Greyhounds are fine with small animals, at least indoors, and those that are not still make super pets for the right owners. We have five dogs, two cats, a toddler aged child, and a snake collection- no issues. Most Greyhounds like to lean on you and get petted. Some love to cuddle. Some are more touchy about their space. Tell the trainer or adoption group what you're looking for... they will find it for you

Not much is sweeter than a big goofy boy Greyhound... except maybe a wise old Mama dawg!
A note about Greyhound PUPPIES. It is possible to locate one, but they are not called Land Sharks without good reason ;-) THEY absolutely need a yard or daily free running. If this is not possible, look for a dog at least three or four years old, with a laid back temperament.
Finally, most Grey folks prefer the term adoption to the term rescue. Those of us who actually work with racing Greyhounds aren't too fond of having our babies referred to as rescue dogs after we've spent years loving them, making their special food, massaging their muscles, worrying about them, and then making sure they have a safe and loving home to go to! When people ask if I rescued my Greyhounds, I say nope. They rescued me! I know there are some bad apples in racing, and I hate them passionately, but we're mostly good people!