I have never made an archer I don't know what skills to use or race

Oblvion has taught me one thing: Khajit, Archery, and Sneak. Sneak really empowers archery with the bonuses, and extra armor with % bonuses really help take the edge off of battles.

Downside: it's much easier to level up and get too strong, leading to potential boredom. That's what happened with me in Oblivion, and once I finished the main quest, I had no desire to "finish" the remaining quests.

I'm currenly at level 40, with barely a third of the main story completed, and I've already leveled up too fast. I'm not bored, but I do miss the challenged of having 6 Draugr coming after me and having to sweat it out my last shot beats their last hit while I'm teetering on audible heartbeats.

I personally always go with a Nord no matter what class I play. Race doesn't really matter. But if you are into roelplaying etc, Bosmer are naturally good archers.

Sneak goes really well with archery. Sneak shots double your damage and triple with a perk you can pick up in the sneak tree.

They benefit a lot from alchemy, smithing, and enchanting. Lots of interesting poisons you can deliver with archery, especially paralysis and slow. Smithing adds a lot of power to your damage.

Bound Bow is a lot of fun if you can get your hands on it. I'm doing a mage play through and I'm supposed to be a destruction mage, but I find myself playing with bound bow a lot. It's a really cool bow. And when you soul trap with a bound bow, you don't get that incredibly loud popping sound.

It's highly unusual to do archery without sneak, because they go so well together, but definitely possible. Somebody made a really fun guide about it recently. http://www.gamesas.com/topic/1366255-guide-to-pure-sneakless-archery/

Expect to feel a bit overpowered, as you'll be killing things quickly as a stealth archer.

My Nord uses archery as a ranged alternative to sword+shield, and does plenty of damage without perks. If he was one-shotting everything, I'd quickly get bored.

I must be in the minority. I rarely get bored with either of my archers and I have found archery to be MUCH better in skyrim than OB.

I have a powerful assassin-type khajiit I fully perked sneak and archery, with little emphasis on crafting still one-shots pretty powerful monsters.

My very weak bosmer archer-thief has only enough perks in archery to get the zoom, but 80+ alchemy she can occasionally take down enemies from a distance with one shot + poison. I use her more to test the limits of stealth and detection though, often I will sneak through and entire camp of forsworn without killing anybody but the quest objective.

But both of them (to stick with the RP) have to be methodical about killing enemies. Take one down, sneak way, return for their friends, etc..

I don't just run into the fray and start peeling caps in svckas.

Bosmer is a good choice.
But once again, race doesn't really matter. It depends on your playing style.
If you're hit-and-running person to avoid enemies melee attack if they are too close, Altmer or Redguard is good choice to running away. Cause Altmer have highest movement speed, and ability Redguard to recorver stamina quickly while running away.
But if you're hit-and-face person, Orcs and Nords and Imperial isn't a bad choices. Cause Orc's ability to double damage for short time, and Nord's ability to make enemy fear and runaway then you can hit them with your bow, and Imperial's ability to Calm your enemies so you can runaway and hit them from afar.
As for perks, you must be don't want to miss Steady perks. It's really help cause slowing time by 25%-50%.
Hope it helps, good luck ^^