It seems like a cab would be the fastest way, but traffic could potentially screw this up, so what's the fastest train route?
You don't have much in terms of options there is The Northeast Corridor line and the NJ Coast Line of NJ Transit that service the Newark Airport and Amtrak's Northeast Regional. The best possible one is NJ Transit since it runs more often and the only possible difference between the 2 is possibility of a single 2 minute stop in Secaucus.
Of course the other option would be to catch a cab or a bus to Newark Penn Station and then you get many many options such as practically every line of NJ Transit, AmTrak, and also PATH which gets you to 33rd and 6th which is 1 block away from the Penn Station.
Personally I prefer the bus which goes to Port Authority $15 every 15 minutes. Which normally would take 30 and in the worst case in my experience 45 minutes to get from Newark to Port. But choice is ultimately yours.
NJ Transit is the most straightforward way. Several trains every hour depart and arrive at NY Penn Station and the third stop from NY Penn station is the Newark Liberty Airport (EWR). The trip takes a bit less than 30 minutes, it is very predictable as you don't depend on traffic, and it and costs $12.50 one-way.