Ah. This is where I come in.
Race: Khajiit
Birthsign: The Thief
Custom Class: Marksman
Favored Attributes: Agility, Intelligence
Major Skills:
-Illusion
-Alchemy
-Marksman
-Sneak
-Blade
-Acrobatics
-Security
Alright, since this is a stealth build, I added in everything a stealth character would need. This is an Assassin build, except Acrobatics swapped with Light Armor. And Intelligence swapped with speed. (My main build)
Basically, you're gonna need Alchemy to make poisons, and Marksman to shoot from a-far. Blade to get you through close encounters, Illusion to help you see in the dark, and a few other things, Acrobatics, to get into vantage points, and sneak and security are self-explanatory.
I chose the Khajiit race because they're statistically the best stealth race from my experience. And favored attributes are Agility and Intelligence rather than Speed is because Alchemy is governed by Intelligence. Although it is only one skill and Speed may have been more useful otherwise, since you have given significance to poisons, I thought it would be best this way.
Hope it helps!