I think both. My cat and I chose each other. I was dreaming and wishing for a magically inclined cat for my birthday over ten years ago now. And I was drawing pictures of my dream kitty. My partner came home one day and said that his friends cats had a litter. I went to visit the kittens and one ignored anything else that happened and would just gaze fixedly at me and purr. She and I chose each other for sure. I dreamt her and she dreamt me and we are a dream together. She is looking out the front door right now at our porch garden.
Sometimes you just go pick out a cat. Those can be a wonderful companion or not. They might just live in your house and tolerate you. Sometimes a cat just shows up and insists on living with you, those are often bestfriends who completely steal your heart. Sometimes you go out and go out and go out looking for the right cat to look into your eyes, and that cat could also be the one.
I think just going to the store and grabbing the cutest cat or the cat that looks a certain way or just a certain breed has less chance of working than looking for that cat that just melds with your energy.
My mom and I both have a knack for finding those purrfect friends.
Thanks for asking me this question, it really means a lot to me actually. My cat and I are like parts of one soul.