All expansions add new items, clothes, actions, etc. but they add more stuff and, personally, more than what TS2 did in their expansions (save 1)
My personal must-haves:
Ambitions - adds a lot of new community lot functions, new jobs with unique mechanics, entrepreneurship (a.k.a. registering yourself as a fisherman, gardener, etc. for your profitable skills), a tradeshop, and expanded existing jobs, Simbot
Late Night - adds more social interactions, more community lot activities, celebrity status and Filming career (splits into Acting and Directing), living in an apartment (although only 1 family can occupy it for some odd reason), Vampire
Generations - adds a lot of activities for the "ignored" life stages (toddler/child/elder), schooling, more community lots, lets you run a daycare, Imaginary Friend. This expansion may seem few but it actually adds a really, really big amount and personally I think this is the best expansion for TS3 next to Ambitions
Seasons - adds season and a more changing weather (it only rains before), holidays, fair activities, adds hot and cold, gives The Sims 3 a really moody feel and feel like they exist in some form of time, Alien
Additives: get these if you want to add more variety for Sim living
Pets - adds pets (dog, cat, horse for sim-like pets, lizard, rodents, and bird for "low end" pets), adds wild fauna (actual interactable but not "acquirable" wild animals), adds various interactions with animals and such, horse racing career, Unicorn
Supernatural - adds 3 life states (Werewolf, Fairy, Witch) but also includes Vampire if you don't have it, and expands vampirism a bit more, adds a bunch of paranormal stuff in the game, Fortune Telling career (career split between a genuine Mystic and a Scam Artist) adds new community activities
Adventuring: get these or some if you want off-world adventuring, you may or may not like them because they put you outside of your original world
World Adventures - adds 3 adventure worlds (Paris/Asia/Egypt versions in Sim world), various in-depth activities in each worlds, can even bring tourists and inherit "foreign" genes, and well... among the three this is the best if you can only pick 1, Mummy
University Life - adds university living during young adult state if you prefer, think of the Sims 2 expansion except a bit more expanded, have 3 cliques (nerd, jock and rebel), most of its stuff really is in that world, adds Sports Agent, Video Game Developer (career split between Engineer and Art Designer), and Art Appraiser (split between Acquisitions and Appraiser), PlantSim
Island Adventure - doesn't "add" a new world but rather adds diving spots and hidden islands on existing neighborhoods (if you bother to put them in), or move to the new neighborhood which has them, can now buy "livable boats" which are essentially "house lot on a boat", Lifeguard career, Mermaid
Into the Future - haven't played much on this yet but focuses on time travel, and any action you do in the present affect the future, with stuff like turning something into a dystopian world or a more pleasant world, Astronomer career (split with Astrophycisist and Space Explorer) and Bot Arena (split with Official and Mechanic), Future SimBot
Why did you make this expansion tier: just only one, essentially the worst of them
Showtime - seriously, why couldn't this just be added with Late Night? All it adds really is just the ability to perform (either singing, tricks, or acrobatics). Genie. I think this was made during the boom of "talent shows"
Now, stuff packs are really just item packs and are worthless unless you want a specific set. With that said, if I am going to recommend something, go get Fast Lane. Adds a huge, huge amount of cars.
