Is there an easy way to get from JFK to the hostel in the early hours of the morning?

In July, I had a similar arrival situation and had a horrible experience with Super Shuttle. So I recommend NOT using SS

Does cost matter? I would say if you want to save some money, take an Uber pool. In the early hours of the morning, there will be very little chance that your Uber driver will have to pick someone else up, but they will still give you the reduced price as if you were picking up another person in your route. I would say the cheapest, but not quite easy is AirTrain, but I'm not sure how frequent the departure times are at that time. You would have to take the AirTrain from JFK to the Subway and then the subway to the hostel.