Incidentally, Uber direct to JFK is slightly cheaper than a cab too ($45-ish?). You think it would be crazy expensive, but it's flat rate. I'm not sure about from JFK into the city, but I think I was told it was the same.
I'm not too big of a fan of the AirTram + Long Island Railway (LIRR) route, which ends up at one of the major train stations, has on outside terminal (not great in the winter and slow with a lot of things to remember to do), but is about half price of that.
I've become a big fan of the AirTrain + LIRR combo since moving into Manhattan from Brooklyn. Almost always consistently 45-50 minutes from terminal to my apartment in Chelsea. Perfect for rush hour to/from JFK.
Uber to JFK is $66 right now. Taxis are a flat rate to JFK as well ($60 plus tip). There are car services you can call which will do it cheaper.
I've recently started doing Penn Station -> Jamaica w/ LIRR -> AirTrain, it's miles better than subway and almost preferable to car if you're paying for the car.
Uber flat price to the city is great until you hit a surge, which is easy to hit in the afternoons, especially when it rains. Then it can be 2x or 3x the price of pre-booking a ride. Uber should add reserve pricing for trips you know in advance, like AWS does.
I'm not too big of a fan of the AirTram + Long Island Railway (LIRR) route, which ends up at one of the major train stations, has on outside terminal (not great in the winter and slow with a lot of things to remember to do), but is about half price of that.