It's true that the E train to 53rd and Lexington (3rd) Avenue is the closest subway stop to the desired destination. However, I'd like to point out that, besides connecting to the JFK Air Train at Jamaica, the E train is also a very easy connection at both Penn Station (EWR train) and Port Authority Bus Terminal (EWR bus).

So it comes down to speed and cost. The Air Train/E Subway combo from JFK will easily be the cheapest option ($7). I would say that it's a tossup in terms of time, so I would definitely recommend using the Air Train/E Subway combo from JFK.