Access the furniture catalogue at robin's shop for 200k after your first house upgrade, opens up most items right away. Pierre's regular catalogue costs 30k, good for wallpapers and flooring if you're decorating. Check robin's rotating stock and the traveling cart regularly, sometimes rare pieces show up there

For themed stuff grab the specialized catalogues when you can - joja's at jojamart 25k, wizard catalogue from krobus, and keep an eye out for the retro and junimo ones at the cart. Movie theater crane game has some exclusive pieces you can't get elsewhere. Special orders from the board, especially robin's and evelyn's quests, give unique furniture rewards

Tip: hitting trash cans 50+ times gives you a 20% chance at the trash catalogue, pretty useful if you're patient. Festival shops often have seasonal decorations you won't find anywhere else

Skip checking the community center or museum for furniture - they don't actually give any except the hero trophy after all bundles. Those secret furniture box rumors aren't true either, though there are some hidden statues around town if you're interested in those

Best approach is getting the main furniture catalogue early, then collecting themed ones as you progress. Late-game stuff like movie theater items needs some patience since you'll need things like the sewer key first