When I was working on my catalog badge, I worked on collecting everything. Furniture, clothing, music, gyroids, fossils, everything that shows up in your catalog at the T&T shop. I'm not certain that all of those things counted, but I figured if they showed up there then it was best to collect them just to be safe.
I think unorderable items count too (e.g. the sloppy furniture series). Just note that you don't need to 100% the catalog. Somewhere around 80% is good enough.