I have always owned cats and dogs, for over 40 years; I have never bought one. All have been abandoned animals, and almost all have no doubt been mixed breeds. I always neutered them, with a couple of exceptions, and I had no problem finding homes for the litters in those cases. I would never pay money for a pup or cat. Way too many out there who need homes.
I have come to feel that mixed breed dogs are much more likely to be good pets and easily trainable than purebreeds. I have had a couple of dogs who appeared to be pure labs, though. I have one now, and she has a lot of medical problems: never dealt with this stuff, like seizure disorder and leg joint problems, with any of the mixed breeds.
The current 4 dogs and one cat do not bother the chickens, some of them hunt and kill rats/mice, and certainly they discourage fox and coon and such from bothering the chickens. I have a small flock that is true free range and have had no losses for nearly a year, despite the local population of such predators.
