Oh, exciting! 
IMO finding the right DOG is more important that the right BREED, although breed specific characteristics are of course important.
We are 6 months in to living with our now 2 year old ground boy.
The learning curve has been steep
but very rewarding.
Although never raced, he has a high prey drive so IME it's not about training but more about innate instinct. Beware.
He is very fixated on me, I still cannot leave the room without him following me to the toilet. Bizarrely, he is fine being left alone for up to 2-3 hours. He goes nuts with excitement when I get home, but seems to just lie on his bed when he is on his own. Neighbours have never reported any whining.
He poos up to 6 times daily 

. Nothing wrong with him, but we are still playing around with different foods. It's a LOT of poo to pick up….
He was neutered, microchipped, vaccinated, wormed and had his teeth done by the rescue we got him from, so has perfect teeth although damaged enamel from chewing the rods of his kennel. Apparently this is not uncommon in greyhounds.
He would chase a ball to the point of exhaustion - he retrieves and retrieves and retrieves
. Nobody told him that he is not a labrador.
Sorry, I am going on about my DDog 
So, ask: ?prey drive, ?what food is she on just now, ?what does the adoption price include, ?what does she value: food or play or cuddles (important to know how to motivate her).
I prioritised working on recall, so ours is not bad now, but I would not trust him at all if there is any kind of distraction squirrels around.
Fwiw, I keep mine on the lead if at all unsure about what's going on around us as I believe that a muzzled, off-lead greyhound can still seriously hurt another animal
Be prepared to absolutely stunned by their speed! And the noise!! The noise they make when they run at full tilt is amazing 
Ours used to be scared of open water - now not so much….