Everyone has one, regardless of your room designs, I'm mainly speaking vanilla game, without welcome to amiibo, but I love the lovely set, it's so cute and I've loved it since Animal Crossing (the first game), and always decorated my room with it!
Well, I love the Alpine and Rococo set. The main season I like both sets is because you can refurbish them to very nice colours. It's really pretty when you refurbish the Rococo set to pink. But I LOVE the Alpine set because you can refurbish the wood colour and the fabric pattern. I love changing the fabric to the wave pattern and the wood to dark wood. It looks unbelievably great in your room. Not sure if it's appeared in any previous games though.
This is gonna be a long list but here are my first ones that come to mind:
Alpine
Rococo
Classic
Gracie
Sloppy
Minimalist
Sweets
Gorgeous
Ranch
Those are the first to come to mind. I'm also a fan of the blue custom on Astro but I didn't include it in the list because that's only one customization that I like out of a whole series.
I know this is predictable, but alpine 4 life! I feel that all the other sets are stuck in one theme forever, but the alpine one... You can change the color of the legs, the pattern on it... You can make it fit into a modern room, a groovy room, an antique room, a cutesy room, whatever!
I love the Minimalist Set (easy to match with almost any room), Sloppy Set (makes any room looked "lived in"), and I also like the Roccoco, Kiddie (pastel), and some pieces of the Weeding Day Set, I guess if that counts.