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Welcome to FT!
There is no rail station in East Brunswick. The New Brunswick rail station (NBK) only has one Amtrak train per day from New York Penn Station (NYP) -- at 6:10
AM. However, NJ Transit has frequent (and cheaper) service from NYP to NBK, as well as service to Metuchen and Edison, in case either of those is more convenient.
JFK to NYP via AirTrain and the LIRR will take about 45-60 minutes. (Buy an off-peak LIRR ticket, unless you are traveling on a weekend, in which case you should buy the cheaper LIRR "City Ticket").
Check
http://www.njtransit.com for NJ transit fares/schedules.
If you want a one-seat ride, check to see if the Princeton Airporter service is still operating: they offered service from JFK to the Hilton in East Brunswick. But the LIRR/NJ Transit option will probably be faster, and certainly will be cheaper.