The cab is the fastest way to go.. but, naturally, the most expensive. Without traffic, it will be a 45 minute trip from JFK to EWR (via Staten Island). Note: you will be charged bridge tolls in addition to your fare.
The shuttles involve a transfer in Manhattan, either at Grand Central or Port Authority.
The train option can be hectic, especially if you are traveling on a weekday.. plenty of commuters on the LIRR and NJT as well as peak-fares. Subway-to-shuttle/NJT is doable but it's a lot of work if you have heavy bags.
The option involves the Q10 is not going to work. Don't even bother with public transit buses.