From Port Authority, it's slightly faster to take a Queens-bound E train (on the uptown platform) to the Jamaica AirTrain station (Sutphin Boulevard), and take AirTrain from there. The AirTrain uses pay-per-ride Metrocards (not "unlimited" Metrocards) for fare payment. You would need a pay-per-ride Metrocard with $10.00 in value for two AirTrain fares. You can purchase such Metrocards at any subway station, or at the AirTrain terminals.
You can avoid the AirTrain altogether -- and save $10 -- by taking the Queens-bound E train to Kew Gardens/Union Turnpike station, and transferring for free to the Q-10 or Q-10 Limited bus, which will take you to JFK Terminal 4. The E train from Port Authority to Kew Gardens takes 25-30 minutes; the bus ride takes about 35-40 minutes, and there is frequent service. From Terminal 4, you can ride the AirTrain free of charge to other terminals in 5-10 minutes.
If you take the E train and AirTrain, I would estimate 75 minutes to get to your terminal; if you take the E train and the Q-10 bus, I would estimate 90 minutes to your terminal. Your individual airline can tell you how far in advance of departure time they want you to check in.
From Port Authority, it's