Bikes can come cheap when you craigslist em. Like fastjake said, if you wanna go out and buy an old road bike and convert it into a fixed gear, it really doesn't take too much. I was thinking about doing this for a while, but decided to go with a complete bike from bikes direct. Got a windsor hour which i put maybe 25 miles a week on and I love it to death. It was cheap, 280 shipped. The components aren't great, but really I'm only like two months into have a fixed gear so I really don't care. Since you'll be new to all this, I would suggest you not invest a bunch of money into a bike that might end up sitting in your garage. It happens to a lot of people. I'm always seeing cl ads that say, bought the bike, didn't ride it.

Now if you feel that you're definitely gonna like the bike, maybe you might want to spend more. Building a bike and selecting all the parts would probably be a lot of fun. And the freedom to customize it any way you want is great. But like someone above said, it's pricey. Even with the cheapest parts you're still looking at $600+ if you buy everything separately. Also, for your safety and for the sake of the bike, it would be helpful to have a friend who knows bikes really well or just take it to the lbs.

To sum it all up...

FG conversion
PROS: cheap, fun to build, need to find the right frame size
CONS: might be a bit ugly, requires bike knowledge

New complete bike:
PROS: Looks pretty, little to no work required (could also be a con if you like the building process), medium priced ($300+)
CONS: Will probably spend more money to customize parts

Custom built:
PROS: It's what you wanted, can't really ask for any more than that, fun to build
CONS: Expensive ($600+), if you can't build it yourself labor costs will be added

I would suggest that you just find a nice BD bike like a kilo. It's moderately priced and it's ready to ride. And if you don't like it, you can probably just put it on craigslist for a price slightly lower than the original and someone will buy it.