If you're new, start with three add-ons at most: 
Questie for quests, 
Pawn to tell you whether gear is an upgrade, and 
Leatrix Plus for small fixes. Everything on this page has a Forever version we've checked. Add more once you know the game. A screen full of add-ons on day one hides what the game is trying to teach you.
The first three
| Add-on | What it does for a new player |
|---|---|
| Questie |
Shows quest givers, objectives and turn-ins on your map |
| Pawn |
Puts an arrow on items that are an upgrade for your character |
| Leatrix Plus |
Faster looting, auto quest handling and other small fixes, all in one panel |
If you picked the Enhanced preset, the game already shows quest areas on the map. Questie still helps, because it also shows where quest givers stand. See Classic or Enhanced.
Three more when you're ready
Leatrix Maps: reveals unexplored areas on the world map and shows each zone's levels. Handy for picking the next zone.
Baganator: one bag window with sorting and search, across all your characters and the bank.
TomTom: a waypoint arrow. Guides and other players often share coordinates, and /wayturns them into an arrow.
Later, not now
- Damage meters such as Details! Damage Meter. Fun in dungeons, but they don't help you learn your class while you level solo.
- Auction tools such as
Auctionator. Useful once you have things to sell. - Full UI replacements like ElvUI. They change everything at once and break more often after patches. See a clean UI with five add-ons when you're ready.
- Gathering maps such as GatherMate2, once you've picked a gathering profession.
Installing them
If add-ons are new to you too, how to install add-ons walks through it, and the add-ons folder shows where they go. If one stops working after a patch, see add-ons not working.
New to the game itself
Our sister site answers the questions new players ask first, from adding friends to what happens when you die: the beginner guide.