As some others have said, I go for pet first, then rarity (my goal is all rare, all level 25)... then, if it is a pet that I would use in pet battles, I start looking for the right breed.
I have certain pets that I would never replace, even though they are the "wrong" breed. For example: Rory (one of my 2 Black Lamb
s) was my very first wild caught rare pet, so even though his breed is less than optimal, he is staying in my collection.
My collection of family specific battle stones is huge, I have multiples of everything except beast stones (of which I still need 5), so if I catch a new wild pet of any other family, I would go for the pet first, then the breed and just stone it once I have the breed I want. I find that having so many stones takes a lot of the stress out of pet hunting as I don't need to worry about finding a rare.