To answer your second question, I've never seen a recruiter that does full-time or contractor but not both. They always try to steer you toward full-time however those full-time positions usually start as contractor-to-hire anyway.
It's really quite easy to find good recruiters in NYC. They are usually subscribed to technical mailing lists and LinkedIn groups. Broadcast your availability and see who contacts you.
One last bit of advice: check out Freelancers Union for health insurance. The options aren't stellar but still better than anywhere else.
What kind of work do you do, if you don't mind my asking?
I've done web development, database design & reporting, email marketing, and a brief stint at a small bond fund, but the only thing I really enjoyed was web development, so focusing back on that now.