Don't use a follower, ever, unless you're going somewhere specifically to kill a dragon (ergo - you won't be sneaking around) and want a mage or some cannon fodder to help you.
Use a bow in the beginning, and carry a one handed sword as well. But stick to the bow, the sword should be for when they're on to you, which will happen fairly often at early levels.
Definitely stick with Light Armour. In fact, you should probably rush to the DB or the Thieves Guild to get their armor as soon as possible.
For perks, I suggest focusing on a couple of trees and not spreading them all over the place. Focus mainly on Sneak and Archery, and when you have the must have perks of those trees (the 15x backstab with a dagger, Steady Hand) start thinking about investing something in Light Armour and Smithing.
You need to think long-term with the perks.
Personally, I'd ignore Lockpicking as you should always have way more lockpicks than you know what to do with and can afford to break loads of them until you beat those Expert and Master locks.
One Handed can be useful and maybe you should put 1 or 2 perks in the initial damage increase, but I wouldn't go very far with it because at some point you'll be so powerful and will be able to sneak so ridiculously easy that you just won't need it anymore.
I've also never found myself needing Illusion spells, because again, if you stick strictly to a sneaky playstyle, your Sneak will increase very fast and you'll be able to literally crouch right in front of someone's face and remain hidden.
That's the gist of it. A useful tip is to remember that you can use arrows as a distraction either to sneak past someone or to get him to turn his back on you for an easy backstab.