You can check in online ahead of time
here to speed up the pickup process. Then, upon arrival, head to the automated kiosk to pick up your rental agreement and head to the lot. It has been a while since we've rented from Alamo at JFK so we're not sure about selecting your own vehicle, but many Alamo locations do support this so there's a good chance.
You can track your Alamo reservation for lower rates by using the link below and we'll notify you if we find a better deal.
Safe travels!