A further suggestion - change your flight from JFK to EWR. Getting to EWR is simplicity itself from NYC Penn Station at any time of the day. All the way to EWR and then just get on the inter-terminal Airtrain monorail thing.
I never bother with JFK now if I'm going into Manhattan
I live in Manhattan and rather fly out of JFK than EWR. I find that the NYC Metro/Subway is much more reliable schedule wise than the trains going to EWR. When going to JFK, I board the F at 57th and 6th, transfer to the E in Queens (which basically means getting off one train and on another train on the same track) and then boarding the AirTrain at Sutphin Blvd. It takes about one hour and ten minutes total for me. Basically JFK and EWR are fairly easy to get to from Manhattan. the difference being that EWR has one "easy" way and JFK has three or more "easy" ways. The problem with JFK is determining which route is the "easiest" for you given your exact location. I think that for the OP the "E Train" to Suphin Blvd. and then the AirTrain to JFK is the best, but there is another route that is slightly faster. (LIRR and AirTrain) (Comes out to only one connection if someone starts with the E or LIRR.)
NYC is not as easy as some other world cities because there are options. Most major cities have one great connection between the City Center and the main airport. NYC has several good connections between the City Center and two major airports. I find LGA to be easy to get to without much luggage, but those with heavy bags would not find it so easy.