I just moved to NYC, have practically the same commute (S. Williamsburg to Dumbo along Kent/Flushing), and am asking similar questions:
http://www.bikeforums.net/showthread...d-tires-in-NYC
Most folks seem to think either that you won't need studded tires or that you should wait & see.

Especially if you're keeping your bike outside, a winter beater is a good choice. Get an old rigid mountain bike (e.g. http://newyork.craigslist.org/wch/bik/2708736128.html ) or road bike with room for fat road tires and put full fenders on it (if you're on a budget, someone posted these incredibly cheap ones lately, though you might want to add longer mudflaps; I got Planet Bike Cascadias). If the derailleurs are acting up, single speed it.

For bike care: oil the chain regularly, spray water-displacing lubricant of some sort on moving parts and steel hardware, and wax the frame with car wax so you don't have to wash off the schmutz as much. The latter two things are often best gotten at auto parts stores.