There's three expansions:
Cities and Knights really expands the base game with additional rules and things to compete over. I would probably get this first.
Seafarers adds extra tiles, a couple minor additional rules, and a bunch of fun scenarios. You can also combine it with Cities and Knights if you want even longer games.
Traders and Barbarians has rule variations and scenarios, including some for the expansions. I'd get this last.
Edit: Keep in mind, you need to also get the 5-6 player expansion for any of the expansion packs that you buy, in addition to the base 5-6 player expansion, if you want to use it with that many people.