I don't use full, complete sets, but use bits from different sets. I use light armor, mostly. Heavy armor, if you're not skilled with it, it will never get you anywhere as a thief or an assassin. You don't need to worry about having a high armor rating if you're good at staying unseen.
Here is my set up:
Armor
A Shrouded Hood, which can be obtained by doing the start up quest for the Dark Brotherhood (choose either side) and while you're in the sanctuary… it's somewhere :P (it's been a while). If you do decide to join the DB, I suggest using that until you kill or save Cicero and get it then. The Shrouded Hood adds 25% better sneaking. Cicero's Hat makes you 35% better at sneaking — extremely useful.
For my boots, I stick with any of them that make you move silently. The one I use, is DB, so another use of DB for great sneaking.
For my gloves, I wear the (yet again, DB stuff saves the day) and use the DB gauntlets.
Now for the fun part of my armor.
For my chestplate… brace yourself… I use Ebony Mail. Yes, yes I know that earlier I made a point against heavy armor (such as Ebony Mail) — I strictly said it was a bad idea. But this Daedric artifact is a totally different story. It makes you pitch black while sneaking (which if you go through the coding carefully, you will find). It makes you a little better at sneaking, during the day out of shadows. But at night, or in shadows you get about 15%. In addition, unlike most heavy armor, it's almost silent. It has one more irresistible trait.
As an assassin, thief, or someone who just likes to sneak around, you will notice that with low armor ratings if you get caught in the middle of an overwhelming situation, which you can't control, cause you're not sneaking, and daggers (I will get into weapons) don't really do much if you're not hidden. But this armor, if you're being attacked, will poison all nearby hostiles.
To top all this off, I have an insanely good ring. I found it when looting some ruin, a Ring of Peerless Sneaking, which means I sneak, 40% better.
Weapons
I use Mehrunes' Razor, which has about the same base stats of a Daedric Dagger. It's one hell of a weapon with its small chance to kill something in one hit. I use this with my Dragonbone Dagger (craftable with DG DLC). For skills (perks) make sure to get 5/5 of the stealth skill (do remember, this checkpoint won't be reached until you are a level 80 sneaker, which will take up many hours of your life). Make sure to get Assassins Blade perk too, and basically focuses yourself on the sneak tree in general.
Powers
Nightingale Embrace of Shadows power is spectacular. Also, I do recommend becoming a Vampire (lord is better, just because a last resort for a thief or assassin (mainly assassin) might need an extra push) if you don't like joining the vamps in DG just ask Serana after or during a certain point in the questline to bite you. (Note that a Vampire/Vampire lord doesn't suit everyone, but comes with major upsides.) As a Vampire, you gain an active effect that makes you 25% harder to notice. Also, if you haven't had blood in a while, it grants you a crazy good power that lets you be invisible (with some other stuff I can't recall at the moment) with the Shadow Stone, and the NG power I mentioned you can go completely invisible 3 times a day. For shouts, Throw Voice.
Misc. Items and Other Tips
I really recommend invisibility potions. I believe it's Chaurus Eggs and Ice Wraith Teeth that you can make your own with (you can get an abundance of both these things early on at Jorrvaskr in Whiterun). It's where the companions live, just look around. Anyway that's what I do, you can literally sneak past everything with all that. Have fun.