You should always make pets you like, but I'm a big believer in having at least two chiv pets of different damage types. They are just very useful and big numbers are fun.
But play around. If you love that wrestling Dragon Wolf, more power to you.
@Khyro has a TON of spiders. he loves them. He went so far as to tame dread spiders in tokuno so he could try bushido on them. We have chiv Skrees, I have poison breath unicorns, discord unicorns, and a whole lot of other unicorns (and I hate unicorns but they are such good pets for a variety of things)
We are both minmaxers though, so we generally want the best dps performance we can get out of a pet. Like a Sampire often plays. So we often play with our chiv pets.
Lots of people like mystic pets, my first trained pet after 97 launched was a mysticism cold drake.