Steam's aggressive auto update of mods seems scary though IMHO. I rarely update a mod if it works, I'd rather not take the risk. Though I cant say I have ever been bit by this.
IMPORTANT TIPS EVERY NOOB MODDER SHOULD KNOW 

1) Dont install a lot of mods at once.
2) Use a fresh save for each mod install
3) back up you saves
4) if a mod has a lot of scripts (quests) or changes meshes /model (the shapes of in game objects) then TEST IT ON A NEW PLAYTHROUGH, not your main character.
5) No matter what someone tells you there is always a risk of corrupting your saves.
That said,
modding is awesome -- a lot of the mods are super stable now, I havent had hardly any issues in a long while.
Must haves
-
SKSE (Scripting helper for other mods. Many, many mods require this)
- SkyUI
(PC Friendly UI)
- Deadly Dragons
- Convenient Horses
- A Quality World Map
- Better Dialog Controls
- Follower trap safety
Some of my other favorites:
Gameplay
- Frostfall
- Cold and Wet
- Achieve That!
- Project Reality - Climates of Tamriel
- Lore-Based Loading Screens
- Amazing Follower Tweaks
- When Vampires Attack
- Footprints
- Guess the Distance
- Auto equip ammo
(or something like that)
Quests
- Dark Brotherhood Resurrection
- Moonpath to Elsweyr
- Falskaar
- Wyrmstooth
Stuff
- Winter Is Coming- Deadly Dragons - Armory
- Immersive Armors
- Immersive Weapons
- Cloaks of Skyrim- Bandolier
(carry more)
- Arise - The Black Sacrament
(armor)
Cosemetic
- Superior Lore-Friendly Hair
- Dimonized UNP
(**NSFW**)
- Natural Eyes
- Natural Eyes - Alternative Vampire Eyes
- Ethereal Elven Overhaul