I've got a rescue saluki x greyhound, he is NOT safe round livestock, generally the problem with sight hounds is they have a switch, it's either off (they are asleep or eating) or it is on, when it is on they just become single minded killers basically, and you can't catch them, they are also pretty much one of the least trainable type of dog in a traditional sense.
Saying this I had a deerhound x greyhound previously from a pup and she was livestock safe, but I did have her from a pup.
I'd say if you get something really really small like a teacup yorkie you should be alright.

In all honesty I think you should get a pup, and invest your time in moulding what you want. As for breeds, I'd avoid sight hounds of any description, I'm not sure it's fair on them with chickens and sheep around. Just go to your local rescue centre and see what pups they've got then take it from there. Anything that has been or is likely to have been stray should be avoided with your livestock.
The advantage if breeders is that (with the right one) you can be pretty sure of the potential of the pup you buy.
Two dogs are easier than 1 in my opinion, but equals five times as much trouble when they decide to mess about
Best advice is don't jump in, the right dog will come along, and when you see it you'll know. My problem is I just keep seeing them, and then I know, and then they're mine