Mutt cats are the most popular as far as how many there are out there and I have one of course but I prefer breeds myself. I wasn't really too passionate about felines until started learning about specific breeds.
Burmese, Abyssinian, Devon Rex and Sphynx are my favorite breeds. I did adore my Bengal but higher ups are for very few people. Mostly I love those breeds because of their more interactive, affectionate, demanding, active and dog like qualities. It could be a problem for some expecting a laid back 'cat attitude' that just hangs out wherever they choose and stays out of the way more often than they are in the way. Many of these breeds are known for things like playing fetch and taking daily walks, tripping you up, stealing objects, and sometimes just being a rambunctious kitten permanently.
I also like the coats, or lack of, on the Devon Rex and the Sphynx breeds but they are also great for homes that can't handle that much kitty fur flying and that the breeds are suited for. I also have owned hairless rats, hairless guinea pigs and like the hairless chinese crested (after 3 Italian Greyhounds needing specialized care I am not ready for another fragile breed) as well so the hairless thing has been known to be something I enjoy but really it's just an added bonus.