I will bring an example of a slightly different Assassin build I made once. It was an Argonian for RP and if he gets caught pop Histskin so he doesn't die so easily. I put a LOT of points into Magicka first (up to 200 or so), then slowly built up Health and Stamina, eventually Health overtaking the other two.
Conjuration - Bound Bow and Bound Sword are the only weapons he used, no Atronachs or Undead.
Illusion - Muffle, Quiet Casting and eventually Invisibility, no Fear, Fury, or Calm.
Alchemy - No Perks at all, just made Paralysis poisons for sticky situations.
Light Armor - Up to Wind Walker
Sneak - 1/5 in the first, then Backstab and Deadly Aim, but NOT Assassin's Blade.
Archery - Up the left side, ignoring Steady Hand.
Ohe Handed - Armsman, Fighting Stance, Savage Strike.
Bound Weapons worked very well since I ignored Smithing and Enchanting. You pretty much have to use regular weapons until you can get the Bound Bow and actually have enough Magicka to cast it. You can start as Breton for 25 Conjuration or High Elf for 150 starting Magicka, both those will help the start. At end game, with Muffle, Invisibility, and Quiet Casting, you are pretty untouchable, so be warned.