The taxi fare is $30 flat rate, NOT including tolls or tip. Usually $40 will cover everything.
The express buses can take a while during rush hour, for instance, but they can also be quite fast at night or early in the morning. During the morning rush hour, they get a special lane on the Long Island Expressway, which helps some.
The helicopters to the old Pan Am building (now MetLife) were cancelled long ago, after a terrible accident in which a helicopter tipped over and decapitated a couple of passengers. There is an East Side heliport at 34th Street, but I'm not sure if anyone makes the trip from JFK. Probably somebody does.
Bruce