Ooooh, I love camping!
Be sure to take large jugs of water - you never know when you might need them. And lots of flashlights for going to the bathroom (there are usually decent bathrooms in campsites these days) at night. And an axe, matches or lighters for starting your fire/stove ... as others said, take more - you never know.
And when you plan your menu, think about cleaning the pots and plates later - you'll have to boil water to do your pots, etc, and you'll need a plastic bucket for washing up. J-Cloths are great for camping.
Spaghetti is amazingly easy (two pots) although the water takes a long time to boil, esp without a lid. Chili is easy, too, for those cold nights. And don't forget about coolers - you can buy those blocks of ice to keep everything fresh or just pack them with frozen food and layer them throughout with no-frozen perishables (cheese, for example).
Coolers take up a lot of room in your vehicle, so I'd mainly buy stuff that doesn't need to be chilled, ie. take frozen burgers and chicken pieces (freeze your own) so they'll thaw over the weekend and you don't need to keep them frozen. Apples and other fruits don't need to be kept in the cooler, buns, crackers, peanut butter, juices, etc are good for snacks that don't need to be chilled. I'd put all the non-perishables in a large box and the perishables in the cooler. You can get away with not having milk for a long weekend - less mess. Get a Bodum if you want coffee...
And don't forget your deck of cards for those nights!
As for air mattresses, I wouldn't bother. You can get really decent thinsulator pads that are comfy and keep the chill off your bod (really a necessity because the ground gets COLD) and are lightweight and roll up very tidily. When I camp and drive, I always take a pillow
Edit: Oh, and corn on the cob and potatoes are good wrapped in foil and placed in the embers in the fire - fantastic, actually.