For Skyrim. Oops.
For me there aren't any game-changing essential mods yet - The rebalancing mods out there are still not to the standard of Francesco's Levelled Creatures and Items or Obscuro's Oblivion Overhaul (of Fallout Wanderer's Edition or Project Nevada).
I wouldn't try any kind of rebalancing mod without playing the vanilla game first, though, so you're on safe ground.
What I would recommend are things which improve what I see as glaring errors. Don't have time for links but everything is on the Nexus - A good alternative bet is to have a look through the Top Files of All Time lists.
You'll need Nexus Mod Manager, SKSE and BOSS before you start. Again, gopher on YouTube has some excellent videos for starting Skyrim modding,
Looking down my mod manager list, I'll give you what I would never start a game without -
A Quality World Map With Roads
Breezehome Ladder Fix - Believe me, this is a real grief saver.
Categorised Favourites Menu
Convenient Horses
Enhanced Distant Terrain
Follower Trap Safety
Guard Dialogue Overhaul
Move It Dammit
Realistic Ragdolls and Force
Shadow Striping Fix
SkyUI
Static Mesh Improvement Mod
Ultimate Follower Overhaul
Unofficial Skyrim, Dawnguard and Hearthfire patches
W.A.T.E.R
Weapons and Armour Fixes
Xenius Character Enhancement
Then there's the free Bethesda HD texture pack which I use now instead of any of the other complete texture replacers, which are ultimately more detailed but just don't seem to 'fit' as well.
You'll probably also want a lighting mod and your choices will purely be based on taste. The top rated ones are Realistic Lighting, Project Reality, Realistic Colours and Real Nights (RCRN) and Ultra Realistic World Lighting (URWL). Of those, my favourite used to be RCRN but I've been getting a bug in the latest release where weather patterns wouldn't change for days on end, but it might be a conflict with another mod. I've since moved on to a little-known lighting mod called No Tint and Desaturation which does exactly what it says on the tin along with darker nights and interiors.
Now I think it's the best of the lot but is a pain to install because it was never packaged properly - If you're confident with extracting elements from different RAR files and repackaging them into one then you'll be fine. There's an explanation in the comments section from a guy who got it working perfectly and I followed his method.