We got a sight hound puppy (saluki x greyhound) last year. I didn't really want a puppy - would have preferred 6 months - 2 years. I looked for about a year in rescues to find one that was small furry friendly but couldn't find one that was reliably OK with all our other (mainly rescue) furries. I specifically went for a very non-working upbringing so he had absolutely no experience of the chase / killing. He was brought up with other animals (mainly horses and dogs, some larger animals and birds). It was also suggested that he was never given soft toys to play with so that he does not make an association with fur and playthings - dogs often rip out the stuffing.
People told me that sighthounds can accept their own pets in the house, but will chase anything outside. This is certainly true for us. I would not trust him off the lead with anything. If it moves, he will chase it if he sees it. He loses all common sense when the instinct kicks in. He likes to run after rooks in a field, but this seems more for fun than a serious chase. I would not trust him with sheep (EVER - bad experience), deer or cows. In the house, I can groom cats or rabbits near him and he won't move. I would never trust him alone with anything furry. All pets have safe areas and there are baby gates across a couple of doorways to keep the cats safer, although he could jump the barriers and dig into runs on grass if he tried. He has never got hold of a live animal before.
Having said that, it is amazing how much he doesn't see / smell when we are out and it is quite easy to be one step ahead. He walks nicely on a short lead and it is enough to prevent him chasing. Other dogs are really more of a problem as he is a very big and very bouncy puppy who wants to play with everyone. Hopefully in another year he will have matured nicely.
We also have some safe-ish places where he goes off the lead - recall is an optional extra still so we are always vigilant and armed with sausages.
So, don't let it put you off - but be wary. Good, consistent training goes a long way to set acceptable behaviour - including a sharp 'No' to any hint of going for a bunny / cat / guinea pig. And sausages.