Hi, 
I bought this day one for PS3 and suffered through the stutter issues. I didn't have a gaming pc at the time. I did every single possible quest in the game and all achievements and then was done. 
I want to buy it now on PC, and I have not played the expansions they released, so I'll be buying Legendary Edition. 
The OP seems like it has not been updated since early 2012. Seeing as how it's now 2 years later... is there a perfect list of stable mods that I should install for the complete ultimate experience?
Also, I hear there is player made content with enough substance it is almost an expansion with in itself. Can someone point me somewhere to get started? A google search brought up a bazillion results, including a few "use these 10 mods" type articles, but I'd really like something like the first few pages of this thread, just 2014'ized. 
Thank you if anybody takes the time to point me in the right direction. I just finished another stint of Everquest 1, and now its time to either replay this or go buy Final Fantasy 14 and play it like a single player game.
		
		
	 
As for the DLC quality mod, I think you're talking about falskaar.
No one can tell you which combination of mods are the best. Just keep in mind going overboard with mods are not a good idea.
I'll try to give you some tips anyways.
For graphics : 
http://wiki.step-project.com/Main_Page
They have very good guide on how to use various programs to install mods the proper way. However, DO NOT install everything they recommend. It is a list of recommendations and you might not like some of the changes it brings.
For gameplay : You have 3 major options:
1) Slightly upgraded vanilla: Look at ACE, Sperg etc. I don't have much experience with them so I can't tell you much. They work well with other mods with minimum number of patches.
2) Skyre: Much larger and diverse perk trees. It is modular so you can choose not to install enemy AI, enemy level scaling, race abilities, combat mechanics etc. But in my opinion, it works best with all the modules installed. However, keep in mind the changes to the weapon and armor are not modular and if you want to use Skyre + other weapon and armor mods, you have to download compatibility patches. There's this cool program called reproccer but that also requires compatibility patches. With Skyre, you can REALLY specialize your character with its excellent (albeit big overwhelming) perk tree.
Skyre generally works well with most other mods with patches (as long as the mods don't change perks).
3) Requiem: a complete overhaul. It plays nothing like vanilla Skyrim. Every race has been changed to match their lore better (or gimped if one thinks of it that way), every weapon and armors value and attack/defense has been changed, every enemy's stats and perks have been changed etc. Enemies and loot don't scale to your level anymore and you'll find yourself running away from bears during the beginning of the game. Game mechanics have changed as well. Arrows often kill lightly armored targets (including the player) in one or two shots depending on the range but are almost useless to heavy armored targets until you get the right perks. The weight of your equipment greatly changes your movement speed so light armor still have their uses. If you want to use magic, robes are actually REALLY useful since light and especially heavy armor raises the mana cost exponentially. Silver weapons/arrows are actually really useful against the undead. Firing ebony arrows on Draugr is like hitting them with nurf guns.
Requiem is horrible if you don't know what you're getting yourself into but it's great if you want old school hardcore rpg with Skyrim's prettiness. However, if you find Requiem too hard, there's an excellent in game menu that comes with Requiem that allows you to change almost everything (Carry weight, arrow damage, damage multiplier, poison behavior, magic behavior, gold/arrow weight, EVERYTHING etc).
Keep in mind if you go Requiem, it is not compatible with almost all mods that changes or adds weapons, armors or enemies and the number of patches available aren't as many as Skyre patches.
Conclusion: Sorry but you'll have to experiment yourself for a week or two before you find the best combination. Just keep a save right after helgen or use alternative start mod for testing. And please don't fall into the trap of trying out too many mods and restarting the game with different mods once you reach whiterun. A lot of these mods really shines in mid and late games.