I've always flown out of JFK for international flights, and I've found them to be helpful. The very first international flight I took as a teen, I got lost, was airsick from an earlier commuter flight, and an airport worker came up to me and found my connection for me and got me a drink. The border people can sometimes be gruff, but the actual workers are pretty brilliant, and if you get over your head, just ask for help.
I seem to remember the baggage all coming through the same place during my flights in the autumn, but since I didn't have connecting flights, I didn't pay attention.