To be completely invisible, take 5 items that you can wear (e.g. amulet, rings, clothes, etc.) and enchant each item with a grand soul gem in the Arcane University Chironasium.
You need at least one chameleon spell learned (and of course access to the arcane) for you to enchant your items.
Each time you enchant it will give you 20% invisibility; so wear all 5 items and you'll be 100% invisible.
When you're wearing all your items it's a constant effect and you can steal, kill, etc without any consequences.
Warning: Don't enchant your weapons with Chameleon, it will only make the person you are fighting invisible.