Either way, you'll be on the AirTrain to either Howard Beach or Jamaica. If you go to Jamaica, you'll have the choice of the subway or the LIRR. Howard Beach is subway.
If it was me & wanted to get the train with luggage, I'd go the AirTrain & LIRR option (depending on the timetable). It's a reasonably quick trip to Penn Station from there on LIRR & the comfort level is higher. Also, the walk to the LIRR is shorter.
You won't pay for AirTrain until you arrive at the transfer station, not the station at the terminal.
For a similar price as the Air Train & LIRR option, you can also get a shuttle such as Supershuttle. I'm not sure if the discount code of NYVAN still works.
When I was there in February, the Air Trains between the terminals wasn't working but they were between Federal Circle & Howard Beach/Jamaica. As a result, buses ran to/from the terminals & Federal Circle. There was no charge for the entire Air Train segment.