For JFK - go to AirTran (two levels above arrival) and couple of stops to Federal Circle.
I mostly do Avis which is very easy - you can by pass counter and pick up directly after confirming your car in their app (refresh for more cars if you are not happy with your choice). Imagine other companies are going to have a similar experience.
Suggest you take the unlimited toll option if you are going across GW bridge (GW bridge is toll by plate). You can use your tag for other toll bridges / tunnels but kinda a hassle to be honest. Unlimited is usually $28-30/day. It’s very easy and you have peace of mind.