Okay, time for a real answer. First of all, a 30-day unlimited MetroCard is currently $76, which is a great deal if you plan on riding the subways (on average) twice a day, every day. (A single, one-way fare is $2, and there are also unlimited weekly cards available so you'll have to do the math for yourself when you get here and see which makes the most sense for you).
Now, as for your rent budget I strongly suggest you get a roommate. You'll be much more likely to find something in your price range in a convenient area if you split the rent. Splitting $1800 (with $900 being your share) is well within the range of finding not just a clean apartment, but a nice one in a great location. There are loads of websites you can check, Craigs list is a good place to start. The best areas in Brooklyn (most convenient to Manhattan) are Brooklyn Heights, Cobble Hill, Carroll Garden, and Park Slope. I'd start with those areas first.
As for a part-time job, that should be no problem at all. The city is full of college students, and most of the major employers understand a school/work schedule. I'd start with the big chains first - Starbucks, Barnes + Noble, The Gap and see which one is the most flexible (moving here in August or sooner also might not be a bad idea, if only to get a jump on everyone else who'll be arriving in September).
The last thing you need to know is that New York really isn't as gigantic as it seems. To the people who live here, it's really just a series of tiny towns right up against one another. People here see their neighborhood as a small, self-contained town in the larger city. So for myself, Brooklyn Heights is my neighborhood, my town, and that's where I live. The dry cleaner knows me, the bartender around the corner calls me by name, the local diner always clears a spot for me at the counter. That's how it really is to live in New York, you live in your little corner of it, and venture into the bigger city when you want.
Best of luck to you. You're about to have the time of your life.