Number 1: Inns & Cathedrals
Buy this firstAdds: 18 tiles with inns and cathedrals, a big meeple, 6th-player pieces and 50/100 point tiles.
Fixes: Lets a sixth player join and adds big-score gambles without much extra rules.
Inns & Cathedrals is the first Carcassonne expansion to buy. It adds a sixth player and bigger scoring without changing the game's feel.
Usually a better fit for a different kind of group — still fine if it sounds fun.