Well im the same way you are, i mainly only go after Rares, but some pets like the Minfernal or S. Welp if you get a chance at one of these and you end up fighting a non rare, just cap it and use a stone on it.
The only 2 wild pets ive ever goten that were no rares are the Minfernal and Festival Turtle, and so far ive used a Aqua stone on the Turtle. I wont use my Magic stone on the Minfernal till i get the breed i want.
Hope this helps.
"I am a soldier, I fight where I am told, and I win where I fight."