The best way to pick a good agent is to interview with several and see what gigs they throw your way. I've gotten a bad vibe off agencies with good clients, and vice versa, so I would ignore any secondary signifiers and look solely at what interviews they send you on. Having said that, I would avoid the big temp agencies. They are clearing houses for cheap temp labor so they waste your time on those stupid in-house computer tests but they don't have good clients for tech.

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?