Couple of bits of advice, based on having just finished my own bike:

1. By your own admission, you're new to this. Therefore, you want brakes on the bike. Period.
2. If you can afford a new rear wheel, go with a track hub - this gives you the option of either riding fixed gear or freewheel singlespeed. There's times when the ability to switch is worth it's weight in gold.
3. Assuming you do #2, ride the bike for a couple of days as a singlespeed. Get used to the bike, then worry about getting used to the art of riding a fixed gear.
4. Shimano Altus. It's a brand/model of crankset, 110 BCD (which is one of the two most common standards) - it's a compact crankset, chainwheels are real plentiful, and the cranks themselves are common as dirt, and very good, serviceable quality. Highly recommended. Check your local second hand bicycle shop.
5. You want brakes. You're not that cool - yet. Attempting to be cool on a brakeless fixie without the requisite skills is a wonderful way to show the general public what an uncoordinated jerk you area - if you're lucky.