Light armor is preferable for a sneaky archer, heavy armor is better for a battle archer. Neither armor type affects archery directly, it's really just a matter of whether you want more stealth or more durability.
Because you don't have to get close to your target, you can rack up sneak attacks easier with your bow, and bows do a LOT of damage per shot, which means a lot of sneak attack damage. At high levels of sneak, you won't even be fully revealed when you hit the target with an arrow, which means you can hit them for a sneak attack, wait a few seconds (the target doesn't need to go completely back to passive), and hit them again for another sneak attack.
Fus Ro Dah.* Know it, love it. You're an archer, which means you get hit rarely (so low armor skill) and you can't block, so you need to keep the enemy off you. The bash attack with a bow (secondary fire with no arrow notched) only buys you enough time to turn around and run, not enough to fire another arrow. Fire/Ice breath are also handy as they stagger the enemy more than just Fus does, but once you get Ro and Dah they're no longer your best disruption choice.
The faster rate of fire perk is a bit broken at the moment. Although it's true you can NOTCH another arrow 30% faster, you need to wait until a normal arrow would be fully drawn or the shot won't travel its full distance. Makes it a bit useless sadly, but it's on the way to the paralyze perk so you'll need to get it.
Even so, I'd say don't bother with the right-hand path of Archery perks. They can't hold a candle to zoom and stagger, and frankly aren't that good even when taken on their own. Even critical shot's damage is only to the base damage of the bow, not the damage it deals in YOUR hands, which means the bonus damage is pathetic. Use enchanted equipment, alchemy, and the base damage boost perk if you need more damage from your bows.
If you're on PC, http://www.skyrimnexus.com/downloads/file.php?id=874 will allow you to break down the tons of low-grade arrows you'll find to craft useful, high-grade arrows. No more firing mere iron arrows from a daedric bow.
Summoning or companions are VERY handy. True, they can get in the way of your shots, but at least they're someone to draw aggro that isn't you. If you're trying to be sneaky, summoning is easier since you can wait to summon until you need the extra protection, rather than having clumsy back there always revealing you, but even companions can just be told to wait a couple rooms back and brought forward every so often, then retreated back to as needed.
*Fus Ro Dah acquisition spoiler
Spoiler Fus Ro Dah is unlocked by doing the first several main quests.