While I am currently living in Florida, I am from New York and have worked
there over the summers that I back home.
The bartending age in NY si 18; however, places in New York City (NYC) might
not hire below 21 for numerous reasons. So, the legal serving age is 18, but
they might only accept bartenders 21 or over.
With regards to the drinks, it depends on where you work. If you work at a
club (i.e. Sound Factory, Exit, etc.), you will doing a lot of shots (JD,
vodka, rum, tequila, Kamakazi, etc.) and simple mixed drinks (i.e.
Screwdrivers, Cran+vodka, pineapple+vodka, JD(or rum)+coke, Long Island Iced
Teas, basically anything with one alcohol and one or two mixers). Any bars
will be the usual (i.e. beer, Cosmos, anything+tonic, Martinis, etc.) That's
usually where I go when I'm in NYC, so anywhere outside of thosed few places,
I can't really help.
Best bet though, go to bar/club/potential place of employment, and sit there
for a while, and get a grasp on the drinks that the place typically serves.
Good luck.