First things first. Do your research. Look at Sheldon Browns site, and ask around the singlespeed fixed gear forums as well. I live in DC and still have the car, but hardly ever drive it. However, I spent money I did not need to when I was setting up my bikes because I did not know any better. But I never had a friend to help me, so thats in your favor.

Like other have said NYC is pretty flat so as a commuter a single speed will be fine. The problem comes in when you want to ride somewhere with hills, then gears are your friends. I have two bikes for just that reason: a fixed gear with a flip flop hub, and a MTB converted utilitarian beast.

As a starving artist, I say get a good SS, either a used bike you can convert or newish. Just realize there may come a time when you have to walk a hill if you get outside the city. I know plenty of people in NYC (actors and otherwise) who dont have a car or a bike so you will be fine either way you decide. Just make sure to get a bike thats fits you well so you want to ride it. Its wasted money if you never ride it because its uncomfortable.