Getting a greyhound is one of the best things I've ever done. She's my best mate and cuddles up on the sofa every night.
I bought all the gear in anticipation of ours and wasted a lot of money. She never went in the crate, ate her beds, ignored toys for a long time.
I recommend a cosy dogs harness, all the others were a waste of time. We have a coat for out doors (if you wear one, so does she).
She has a fleece onesie to sleep in, in winter, plus a couple of jumpers that people have knit for her.
Don't buy any clothes that aren't meant for greys, they will be too big on the chest and probably not long enough.
Ours was too timid to race and has no prey drive. She went up to sniff a cat, which swiped her and now she's terrified of all cats.
She's very anxious when out, something will freak her out and set us back. Consistency is key. She used to refuse to go for a walk but I put her harness on and took her anyway. She is not keen on other dogs so if she's off lead, I put her back on if one approaches - she has been known to run home.
If you're on Facebook, there's a good group for retired greyhounds. They've been very helpful with advice in the past.
Feel free to PM