At that hour of the night I'd grab a taxi. Luggage in the trunk, three in the back, one in the front (unless you get a minivan cab but you don't need to wait for one). You get your bags, walk outside, and the cabs are there.

Any of the car services would give you the pricing up front, you call to let them know you will be needing a car, though they are probably already there, and when you get in you call and the driver shows up a few minutes (hopefully) later. There's no guarantee you will get a better car then a taxi at all.