Get with a private that could lead you to a 911 promotion:
Seniorcare EMS (KBJ + BKH contracts)
Transcare (I hear their in trouble though) (Bunch of bronx contracts, NYU, etc)
Hunter Ambulance (NYHQ contract)
Get with a private that does emergencies to non-hospital healthcare facilities (assisted living, SNFs, docs offices):
Seniorcare EMS, Transcare, RCA
If your into alot of dialysis calls and not too much emergency action: Midwood, Lifeline, Priority1. I don't know about the other "little guys" in NYC ie citywide, firstresponse, primary care, etc.
Also Volunteer to get STREET experience. I'm talking about MVAs, peds struck, etc. The only other way you would get street experience is in a private when you get flagged down, or you stop and ask if someone needs help, especially at an MVA and no EMS is there yet.
I've seen some hospitals put 6 months minimum, I'm going all out applying everywhere once I hit my 6 months, and the volunteer experience wouldn't hurt either. LIJ I hear hires without experience.
Don't listen to the naysayers on buffing. There are experienced folks in volunteer ambulances who will show you the way. Just don't buff at a private ambulance