This is what I personally would go with if you wanna be a thief type archer.
Skyrim Perk Calculator - Plan the perks for your Skyrim character before spending them!
Archery - Set to maximum damage & perks
Smithing - Set to allow you to craft and improve all the light armor types as well as improve enchanted pieces.
Light Armor - Best armor type to use for a sneak thief as it makes you lighter on your feet thus less likely to be detected. Set for maximum armor boost, faster stm regen, & 10% odds of not getting hit by attacks at all.
Sneak - Sneaking isn't that hard w/ light armor so the 20% boost should be sufficient. Sneak triple damage bonus for bow can add a lot of damage. You can prevent traps pressure plate traps from triggering and reduce your noise further which will reduce detection chance.
Lockpicking - Improve the loot & gold you can find in chests. Set to make all but master locks easier to pick. Picks start close to opening position will make opening any lock type simple. Unbreakable picks will render master lockpicking moot since you can just keep rotating the picks until you find the combo without losing any picks at all. Can pick locks without being detected will allow you to steal so many things in chests or break into places without being detected.
Pickpocket - Pickpocketing isn't that hard in this game but going into this tree will allow you to steal money, keys, equipped weapons & armor from non-hostile targets. If there is a target that has something you want but low odds of stealing it then just save prior to trying to steal and reload if you get caught until you don't get caught. Can also enchant for higher pickpocketing odds.
Speech - Can get away with crimes a little easier by bribing guards and persuading people otherwise. Additionally you'll be able to sell anything to anyone thus allowing you to bring your stolen goods to anyone for some easy money. Also will give you more money from said people and allow you to buy anything from them for cheaper.
Enchanting - Stronger Enchants for your equipment & allows you to put 2 enchants on every item rather then 1. Very very handy to have.
