Hi Chrissy 
I have in the past worked in racing kennels for 8 years, 
Greyhounds make great pets, i had one for over 10 years as a pet. 
but rember they will need house training,  they make great pets and are so 
happy to just lay about and love attension.    
Would like to also point out that the kennels that i worked in never put a dog 
to sleep after they had finished racing, they where all rehomed, and if the new 
owners had any problems with them they came back to us to be rehomed 
again.  some people do not rearlise they can dislike cats and very small dogs.   
if you do have another dog then take it with you to the kennals then when you take a dog you like for a walk you can introduce them to each other and 
see if they will get on,  my other bit of advice would be to make sure the 
greyhound is muzzled when you take it out for walks until you are happy 
that he will do what you want him to do,    
Hope this is helpful to you 
And good luck    
Ray