Starting from London, the quickest option is to take BA1 from LCY to JFK on the "babybus". That undergoes pre-clearance at Shannon in Ireland whilst refueling, and so lands as a "domestic" flight. Hand baggage only, you can get from jetty to cab/taxi in under 5 minutes (3 isn't impossible!)
Next quickest from the arrivals perspective is to fly from London (any airport) to Dublin, and connect there onto a flight to New York. All US-bound flights leaving from Dublin are pre-clearance flights, so you'll go through US immigration + customs in Dublin. You also go through US-compatible security re-screening in Dublin too, so you pop out in New York as a "domestic" arrival straight into the terminal. If you have onward connections, this makes a big difference, as you can just walk to the next gate
Otherwise, the question isn't what airport, but what terminal. It's no good deciding that JFK is great if you then book on an airline that flies into a terminal with no automated APC kiosks, for example!
Finally, consider other flights arriving at the terminal at the same time as you. If your flight gets in 20 minutes after two A380s just pitched up, you're in a long queue. If your flight is the first international flight of the day to arrive, you're probably fine.
Oh, and consider Global Entry if you travel to the USA a lot - it'll get you much quicker immigration, often a quicker customs line, and it'll get you TSA Pre which means quicker security on your departure.