So this is the first time i'm running a thief character. I went with Khajiit just because they have +10 to sneak.
I've not really got much of an idea what skills I should use to make a decent thief and which perks to take. I'm currently level 12 and haven't spent any of my perks yet, so I have 11 spare.

As far as combat goes, I was gonna go with Archery or Daggers due to the high sneak attack multipliers. Is this a good idea?

Also, should I be increasing health, stamina or magicka? I heard Illusion is quite a decent skill for thieves.

I've been running a very similar character, bosmer thief bows daggers and light armor currently level 49. It is totally awesome the trees you should focus on are: Archery, One-handed (for the arms-men and dual wielding perks), sneak (for the anti-detection bonuses and critical multipliers) and light armor. I also put smithing into the mix so i could make my own light gear but that's probably not essential. I have never used any illusion spells except for candlelight and very rarely clairvoyance and I have not missed it.

In terms of level ups I did (for every ten levels) stamina:4 health:4 magicka:2 worked pretty well

Well, I am new to the game and have been running my first character as a sneaky thief/assassin with fair success since Christmas. So for what its worth this is what I did.

Having also gone for a Khajiit, I put my perks into Sneak and Archery pretty much equally and one handed weapons when I had a perk to spare. I didn't touch daggers until I got the 15x perk. I am now at level 28, I can sneak past/behind just about anyone/anything that isn't sitting in a circle of bright light, drop most enemies with one arrow (Deathlords and the like excepted) and regularly enjoy the cut-throat animation. I haven't touched or used, alchemy, magic, enchanting or smithing at all - though I am starting to think I might do well to put some effort in at least two of those in the near future..

I wear light armour (a mixture of TG Guildmaster's, Nightingales', and DB) but put no points into the light armour perk-tree nor did I invest in lock-picking. Both those skills seem to level up quite nicely on their own.

For what its worth.

In my opinion you are going to want at the very least the "Agile Defender" perks from the light armor tree. There are enemies dragons for instance that cannot be dropped from sneak and if you are ever found while sneaking past forsworn. You will be in a world of pain and misery unless you invest in that extra protection.

My Thief/Assassin focuses on One-Handed, Archery, Light Armour, Sneak, Smithing and Enchanting. Smithing and Enchanting aren't required to function properly, but they can help. I have considered investing in Illusion, but decided against it because killing things is easy enough already, what with the Sneak multipliers for daggers and bows. Investing in One-Handed, Archery and Sneak are therefore going to be your priorities.

I never, ever, used magic on my Assassin, so instead I focused more on health and stamina. By now (lv 45) I have around 350 health and 250 stamina, and that works quite well (long sprinting duration and enough health to take a hit). Priority is health, more stamina is mostly a novelty, but a very useful novelty at that.

A fair point. I haven't been killed by a dragon yet, and the Forsworn have not caused me a major problem. However, I shall take your advice and put some points into getting the agile defender perk.

Thanks for all the great advice so far. I think i'll level pickpocket to at least 50 to get the extra pockets perk as i'm always over encumbered with stuff.

Fadecy, one last point from me. Have you played as a Khajiit before? If you haven't you might be shocked by the number of gratuitously offensive comments directed your way by guards and "normal" citizens. So far I have managed to keep my temper but its getting harder and harder to do so. In fact, the next person who calls me a thief (an outrageous remark as I have never been caught), a cat, or mutters "meoww" under their breath as I walk past, is going to feel my claws and be damned to the bounty.