You have a number of options:
Taxi is $45+tolls+tip and takes about 45 minutes+ depending on traffic.
NYAS express bus is $15, same time as above.
Subway E from Jamaica Station is $2.25, takes about one hour.
Long Island RR from Jamaica Station is $8 peak/$5.75 off peak, train has overhead luggage racks and is faster than subway, takes about 20 minutes.
Airtrain to Jamaica Station is $5, takes about 15 minutes.
My suggestion is LIRR, if your timing is good on the Airtrain and LIRR you could go from terminal to Penn Station in about 45 minutes.
You have a number of