hi Suzanne - welcome to the forum! You will be delighted with a basenji once you get one. I found that tons of research, both on the breed and different breeders, helped me out tremendously. Other than the breeder doing lots of health testing on the parent dogs, look for a breeder that also concerns themselves with temperament. That worked out very well for us. The other thing I would say is the breeder should state, in a contract, that if for ANY reason you cannot keep your basenji, it should go back to them (cannot be resold by you). For me, this was really important. It proved to me that our breeder really cared about the pups they were placing.
Just thought of another thing - be wary of a breeder who does not want you to visit them to see their home/dog area. That would be a red flag for me. And understand that a good breeder will really interview you, and may want to see pictures of your home, backyard, etc. to make sure the pup will be in the safest environment possible.