Ok,

Just to summarize and clarify the trains...

The EWR Airtrain goes to a station called Newark Airport on the NE corridor, at which you can get NJTransit trains to New York Penn Station

(Amtrak trains also stop there, but they are no faster and about 8 times the price, so not worth it!)

The NJT trains/Airtrain Combo costs approx $11.75 (may be more for peak times) and run about every 10 mins. I would allow at least 45 minutes for this leg, but sometimes it seems much longer (at times like you could get out and push the train to make it go faster... not sure why) so I would count about an hour.

The NJT train WILL be crowded with rush hour commuters.

At NYPenn, you come upstairs from the track to the main NJT/Amtrak concourse, then have to go down to the lower level to change for the Long Island Railroad for a train to Jamaica station.

If you go to a vending machine, you can buy a combination MetroCard/LIRR ticket. It's a nifty little contraption with the Metrocard magnetic strip on one side and the LIRR ticket on the back.

The fare is $4.75 for the LIRR plus $5 for the JFK Airtrain. The combo is an option on the screen.

Stay near the front of the train and when you get off in Jamiaca there will be an escalator and elevator up to the Airtrain concourse. Swipe the flip side of the combo ticket at the turnstiles and you are there.

The LIRR to Jamaica is around 20 minutes (and should be relatively calm except for some reverse commuters.) The Airtrain is about another 10.

While you are on it, look down at the road below and the people sitting in traffic. That's the infamous Van Wyck Expressway. This is my favorite part of the journey...

As others have pointed out, there are cheaper ways to do it, but they are not as tourist and bag friendly - not well marked, no elevators or escalators, longer, etc. - IMO.

This way you can pretty securely do in about 2 hours and should avoid any real rush hour delays.

BTW, if you do take a car of any sort, the driver will probably know this, but make sure you don't go through the city. Have him go via Staten Island and the Verazano Bridge. You will still hit traffic, but you will avoid delays at the Holland or Lincoln Tunnels.

Good luck