On the rare occasions when the cat(s) have not come to me, I have chosen those who are usually overlooked: who are shy, fearful, old, not quite healthy, injured or disabled, or otherwise most in need of love and, well, being chosen.
I have found these to be the ones who give me the most joy. Seeing them find themselves, find their place, start to bloom and to come out of their shells, turning into vibrant, loving beings, is profoundly gratifying! Many who come to us have been traumatized, abused, alone, unloved. These are the ones to consider when you are "choosing a cat"!
* This goes for any animal companion!