I always wait for the right cat to PICK ME, as one person mentioned above, even if he/she is a bit on the beat-up-looking side. I fell for one little lad a few years ago with one eye missing, and half a tail. I was dead set on adopting him, when another kind couple snatched him up first...apparently he knew how to "work the crowd"! Make sure you're able to interact 1:1 with each cat, and get to know how he/she does around other cats, dogs, small children, opposite sex humans, etc. Does the cat seem well socialized? How does the cat fit into your lifestyle? In other words, if you work and are gone for most of the day, a kitten may not be the best option. You may want to opt for a lazier, more independent adult that can tolerate some alone time. I do tend to overlook health issues, as those are issues that tend to improve dramatically once a cat has found an owner that gives a damn. When I first adopted 9-month old Fergus, his tail was broken, he had a wounded paw, his ears were infested with mites, he was NOT neutered, he had an upper respiratory infection, and conjunctivitus in his eyes. He was rough looking little guy, and needed a good bath to bring out his beautiful white fur, a vet visit, and about 3 different types of medication to bring him to good health. What stood out for me about this cat was that he was AFFECTIONATE, and seemed to be connected to me right from the start...he was instantly my best friend. After about 3 weeks of tending to his ouchies, getting him neutered, vaccinated, a nice bath, lap time, play sessions, a roof over his lovely head, a quality diet, and endless smooches, he turned out to be one handsome fellow...who would have known?
THIS is what you look for in a shelter kitty...and once you get there, and spend time with the cats and learn about each one and their histories, it either becomes really difficult to make a choice, or incredibly easy.