Most Borzoi breeders are serious ones; they want their puppies to go to good homes and only want the best for their Borzoi. The Borzoi is not so rare that most people can't find a Borzoi breeder within driving distance. This may or may not be the best breeder for you, so keep that in mind when purchasing your Borzoi.
A good breeder usually only breeds once a year, if that, so be prepared for a wait for your puppy. It will be worth it. Some breeders network with each other, and it is not uncommon for them to recommend another breeder who they respect if the wait will be a very long one. Most breeders nowadays have a bitch or two who live in the house, and that is actually preferable to buying a puppy who only lives in the kennel. Most breeders will be more than happy to discuss pedigrees with you, so be prepared to be bombarded with photos and pedigrees and win ribbons. I would be more concerned with the breeder who looks sort of blank when you try and discuss the puppy's ancestory. THIS is NOT a good sign!
No matter for what purpose you are getting your dog, you should be concerned about health and longevity. The breeder should have some older dogs running around the yard, unless they are very new to the breed. Some health concerns are torsion (bloat), kidney problems, eye disease, cardiomyopathy, and auto-immune problems. Some of these are not directly inherited, but there may be some concern if several of this breeder's dogs have died from the same problem. Ask to see eye certificates from certified veterinarians of the parents of any pup you are considering. Hip certification is less important. Some breeders feel that Borzoi should have their hips x-rayed and others do not feel it is important because the incidence of hip dysplasia in all sighthounds is very low. All puppies should be started on the leash and have had some house time, especially if they are older.
Do not discount an older Borzoi. Many times, if well socialized, they adjust well to their new life. Older dogs can be an advantage, too, over young pups. Older Borzoi are not as destructive as small puppies. Borzoi are also unique in that they need vast amounts of exercise as puppies. If they don't get a place to run full out whenever they want to while they are growing up, they may well grow up to be spindly, under-muscled adults. If you can't provide a Borzoi puppy with a large, fenced yard and perhaps a companion to play with, an older dog can be a good choice. If you are searching for a show prospect, and older dog is even better. Puppies can be a gamble, even from a good breeder who knows their lines. Too much growing is ahead for a very young pup. In an adult dog, what you see is what you get.
If you are in particular looking for a good running dog for lure coursing, keep in mind that many dogs from different lines run well. But in some lines, more dogs run after the lure than in other lines. This tends to be at least in some part an inherited trait. If this is something important to you, please ask the breeder about the running history of the kennel. Don't accept a mumbled, "My dogs LOVE to run, I just haven't had time to lure course," explanation of their dogs' lure ability. Those breeders who are serious about lure coursing have titles or ribbons from coursing events to show you and have evaluated the litter for coursing potential.
A good breeder will require all stock that is not breeding quality to be spayed or neutered, and will only provide a limited registration for those puppies deemed companion quality only. It is VERY rare for all pups to be breeding quality in a litter. Even in really top litters, most breeders will sell some puppies on a limited registration. Please keep in mind that Borzoi are not the easiest breed to sell. A good breeder will realize this and protect their bloodlines from unscrupulous and haphazard breeding by using the limited registration. Even though you may be paying what you consider a good price for your new Borzoi puppy, don't expect to be able to breed it and sell every puppy at 8 weeks of age for what you bought your puppy for. Borzoi are notoriously hard to sell (if you are choosey where they go - and you SHOULD be - every puppy is your responsibility until they die!). They also lack the cute fuzzy stage that most dogs go through, and can be very homely just about the time they are ready to go to their new homes. Most breeders end up keeping several puppies for several months before they find the right home for them. Nothing can eat as much as a Borzoi puppy (and, consequently, what goes in, must come out!).
Be aware of co-ownerships. These can be good and bad, and depend on a large extent how well you get along with this person you are buying your puppy from. Most of the breeding co-ownerships are really hard on all parties involved. Buying outright is sometimes ideal, but some good breeders may want to co-own with you, at least for a time, especially if you are new to the breed. They only want to protect their pups from being breed irresponsibly (I know, YOU wouldn't do that, but they are not so sure!) or from being passed from home to home. Evaluate the reason why the breeder wishes to co-own a dog with you. Is it because they are concerned about their precious puppy and are only trying to protect it? Or is it because they have found someone they think they can use to produce puppies for them. Think about it. Most Borzoi people, thank goodness, are only trying to protect their dogs, but there ARE some sharpies out there. If you get a bad feeling about a breeder, remember, you are not obligated to buy from them. Go somewhere else.
Remember, the breeder you buy your pup from will be sort of like a relative, in a way, and if you feel uncomfortable around them, this could be a bad sign. Good breeders will want to keep in touch to see how well you and the dog are getting along and encourage phone calls and letters.
I get really turned off when a breeder gets pushy or swears their dogs have no faults, and you should be suspicious of any that make outrageous claims for their dogs. Under no circumstance should you buy a dog from a PET SHOP, that pretty much should go without saying. But some breeders are little better than a pet shop - just cranking out a litter of pups for their egos or whatever. Avoid these "breeders" like the plague! Thankfully most Borzoi breeders DO seem to have the breed's welfare at heart.