I'd take that little kitty, that cute dog, a horse, a tiger, a lion, a puma, a bear (the little one) and of course a coala bear, and a panda, and a green dragon, then a phoenix, also one hippogriff, and a... I love animals except birds (I like owls, hawks, eagles...), insects (I'm afraid of butterflies), reptiles...
OK, and now seriously, I'd choose a horse, but the most... the best of the best, very expensive, but very nice, of course, it wouldn't be actually "a pet", but if I were to choose...
By the way. have you seen a cartoon, I don't remember the name, well, it's about the family of four polar bears in the zoo (dad, mom, son and uncle), very funny, especially when the son says: "Mom, the giraff and the polar bear... hm.. it's not natural!"
If you lived in the Middle Ages, what would you do?