Probably just my rococo and princess sets. Everything else I could easily get back, but those took the longest to get and I like them the most.
I don't think I'd ever reset though.
The only thing stopping me from resetting in my second town is my villagers. I am none too thrilled with my map anymore. I wish I could just tell all the villagers we're moving to a new town and start over..
I reseted once, and I wanted to bring my mannequins with me. That of course was impossible. I took the Hero costume, Samus costume, some of my Zelda items, my Metroid, and that was about it.
I guess if I DID then I'd keep my unorderables, bells, and golden tools. Wouldn't worry about villagers, landscaping, or anything I could catalog again.
I didn't bring anything with me when I reset, but I'm not going to reset again because I am so happy with my layout and I have two of my favourite villagers (Freya and Rosie) ^~^ I think if I did reset though, I still wouldn't bring anything because it's better to start over fresh in my opinion
I'd bring Fang with me. And to make sure I don't forget, I'll pack him in a suitcase together with my tools,12 million bells, my monocle and my tophat with me.