As a general rule, you can take a metered cab from JFK to Long Island and pay twice the meter. There used to be (and may still be) airport limo / shared ride services that operate to specific hotels.

Luggage may be a hassle, but the cheaper way to go would be to take the bus that connects JFK and LGA and get off at the intermediate stop at the Jamaica LIRR station, from which trains go to Long Island.