Welcome to Flyertalk.
I use airpark at JFK,
www.airparkparking.com. They are $20 a day with tax, and give you one or two free days for every seven depending on which coupon you have. Just used them last week, they drove us immediatly over to the terminal, and took about 15 minutes last night for a pickup (they were totally sacked at once, they had two vans that were filled as everybody came in at once).
On airport parking is $15 a day in the long term lot.
Driving to JFK can be a breeze or it can be a nightmare, and there's no way to tell which it will be at any given time, so leave plenty of time. You may get there very early, but that's way better then getting there very late.
Even if you use the onsite long term, consider getting a reservation at one of the off site lots just in case the onsite stuff is full. Most of the off sites are very packed, and you need reservations. Better to have one and not use it then to need one and not have it.