I am planning to take the AirTrain from JFK to Jamaica station and an LIRR eastbound (to Stony Brook).

How do you suggest I pay for these rides the optimized(read cheap) way??

I am new to NY, so I don't have the metrocard with me. Paying for the AirTrain at Jamaica with a pay-per-ride metrocard, would it incur me the $1 card cost? If it does, can I use the same card to buy the LIRR ticket?

Can I take these rides without ever buying the new-metro card?

Is there a combo ticket I can purchase I can use both on the AirTrain and LIRR?