For my first play through I'll be playing a Khajiit archer/thief/assassin.

I have the backstory written and a name selected, now all I need are my skills.

If you were in my shoes what skills/perks would you pick? and why

Archery, Sneak, Pickpocket, Lockpick, maybe One Handed, maybe Light Armor, maybe Illusion

The Sneak and Illusion will keep you hidden and allow you to do sneak attacks with your bow.

Archery, since bow is your main weapon. One handed to finish off those who don't die from the sneak attack, or if you find yourself in close quarters.

Light Armor to keep you alive and help you regenerate stamina.

Well, it's pretty obvious. Light armor, archery, one-handed, sneak, alchemy (poisons), lockpick, pickpocket.

But you don't have to PICK em; those are the ones you'll be using if you play according to that playstyle.

After that, it's really up to you... might want to use speech, illusion, smithing.

I choose skills based on raw combat, since I consider everything else unnecessary diversions. Skills like lockpicking, pickpocketing, and speechcraft are good enough unperked (or at least I hope they are.... I wouldn't put it past the developers to nerf a maxed skill as useless when unperked).

( Health 300 / Stamina 400+ / Magicka 100 )
Perk Total: [51-72]

Major Skills:
1) One-Handed (15 Perks focusing on "Swords"/"Dual wield") ~{DPS for assassinations}
2) Archery (16 perks on everything) ~{Archery is stated as your main archetype}
3) Sneak (13 Perks on everything) ~{Optimized Stealth}
4) Light Armor (7 Perks on "Agile Defender"/"Unhindered") ~{can replace this skill with another of choice if you don't care about armor}

Minor Skills:
5) Enchanting (0-11 Perks focusing on "Weapon Damage" and "Armor") ~{Improves your gear}
6) Smithing (0-10 Perks focusing on "Weapons") ~{improves your gear}

Miscellaneous Skills: [No Perks]

~Block
~Speechcraft
~Lockpicking
~Pickpocketing
~Alchemy

The key thing to remember about Skyrim is you do not need to focus on skills as much as the perks you plan on taking. Of course high level perks require high skill level. You have a broad focus of assassin/archer/thief. I would try to decide on whether being a deadly assassin or an opportunist thief is more important. Do you want to keep things "pure" or mix in some magic as well. Sticking with Archery as a primary, wanted skill the assassin would be skilled in Light Armor since occasionally you will be cornered and outnumbered and want some protection. One handed skill for these up close fights, Sneak for getting to the target, Alchemy for deadly poisons and restorative potions (if you play Bosmer the snakeblood perk will make you immune to poison), and lastly Lockpicking to bypass locked doors to your target. A pure thief character may replace one combat skill with Speech or Pickpocket or even take both at the expense of alchemy as well.

Just my two cents...

I took the perk approach. Ill PM you which ones if you want but....

Archery
One-Hand
Sneak
Pickpocket
Alchemy

Perks work out nicely and you take full advantage of racial bonuses.

This is intended for thievery too, if your focused on Assassin purely or want to stand and fight a bit more exchange Pickpocket for Light Armor, or for a bit of magic Alteration.

My build is:
Archery (12)
One-Hand (11)
Sneak (10)
Pickpocket (9)
Alchemy (7)

My first recommendation is to play the character naturally, and let the actual role-playing of your character decide what skills he uses. When making decisions between what tools to use, how to complete an objective, or even which direction to travel, consider the question from the perspective of your character and your skills will level up accordingly.

Regardless of whether or not you want to roleplay that heavily, its always good to have a plan! (I'm sure your Khajiit would have one...) So the obvious choices are archery and sneak. These will in all likelihood be your primary skills which will level up the fastest and you will probably spend the most perks here. Secondary skills could potentially be pickpocketing, alchemy, light armor, one-handed, or lockpicking. Since you are playing both an archer and an assassin, your gameplay style would benefit greatly from Alchemical poisons, this also fits in nicely with your character. Now I think it will be in your best interest to keep a shortsword or a dagger with you, but that doesn't necessarily mean it needs to be one of your skills - unless you want it to. Based on the kind of character it sounds like you're going for, I think pickpocketing, lockpicking, and light armor should be your secondary skills.

The interesting thing in skyrim is the perk system, so you have the option of having 4 primary skills that will use up almost all of your perks, 2 primary skills and 4 secondary skills (skills with some but not all of the perks) 6-8 secondary skills or really any combination.

My character will put almost all of his perks into 4 primary skills, deciding how you want to spend your perks might help you choose your skills and decide your specialties.