I love the pets idea! I'm going for an all specific villager town right now but once I accomplish it I will probably change things up and go for more variety. I think both are fun ideas but having a variety of different villagers makes things more interesting for sure!
Go for variety, or some of the less conventionally cute villagers. Some of my favourites are the anteaters, ostriches and sheep, which I find far more appealing than the generic cuddly-looking bear cubs or the villagers considered prettier, such as Diana and Merengue. The mice are sweet too, especially Bella. Adorable punk rock mouse? Yes please.
I like the idea of the pet town. I'm not too crazy about all of the dog villagers, and have a pet centric town will give you more options and a more diverse town while still having a cute theme!