I've had rescue greyhounds successfully (and one lurcher much less successfully). I am sure you've researched the subject, and know all about them, but I'm happy to answer any questions you might have.
Greyhounds are fairly placid and loving, but occasionally a bit 'needy'. They can be lazy, but don't need a lot of exercise to keep fit enough (though obviously not at racing fitness).
Key issues to remember:
Racing greyhounds are fed sloppy food. Their teeth may be in a shocking (and expensive) state, as may their digestive systems. It may take a while to find something that suits them.
They've never learned to play. They can pick it up later, but one of ours, while she was taught to have a gad about by the other dog, never had a clue why anyone might be throwing sticks or balls.
But, as I say, if you have the time, space, resources and support, a greyhound makes a lovely companion.