A trick I found handy for food is two coolers, one for stuff on ice, the other for meats put on dry ice. This is really only useful when you're camping for three days or more. If I know we're gonna have steaks that night I'll take them from the dry ice cooler and put them in the ice cooler that morning. Meat can turn fast, especially in summer camping months. The dry ice idea also seems to cut down on the need for as much regular ice. Also, don't go cheap on coolers. The better the seal, the longer your ice will last, reducing the trips for ice. This all really only applies to car camping.
As for tents, I keep two. One sleeps 8, the other sleeps four. I never really camp with more than one other girl. The 8 person tent was handy when I dated a girl with a Doberman. We fit all of our packs, queen airbed, and dogs.
The four man tent, which in my opinion should only be used for two people, is what I use when I'm hiking in.
As someone else stated, get tarps. Nothings worse than finding out about a tents weak (read: leak) points in the middle of the night with no way to compensate for it.
Also, for car camping I like to use a pop up canopy. On camping trips where the weather turns rainy those things are invaluable, and help keep people from being miserable.
My most favorite piece of equipment for camping is a clip on hat light though. You can get an el cheapo $5 light from Walmart, or they have some models for $20 that you can replace the batteries in. Beats carrying a flashlight in the woods at night when you need both hands for cooking, gathering firewood, giving your lady some sweet lovin', etc.
As for pots, pans, etc. Dutch ovens, cast iron pans are nice, but you really do need to maintain a hot fire to use them correctly. Personally, I usually bring my own firewood in. I know that sounds retarded, considering you're in the woods. However, most areas are picked clean of firewood, or the wood may be wet from a previous storm. In some cases, the wood may just be shit for fires (pine). Pre cut wood burns more evenly, allowing you to maintain more consistent temps for cooking.
Don't take any pots and pans you can't afford to lose or have destroyed. Camp fire will blacken any pot or pan you use, no way around that really. They say you can rub the outsides of pots and pans with bar soap so the black washes off easily later, but that's such a pain in the ass.
I invested in a nice stackable/nesting pot/pan set. It compacts nicely and sits inside a mesh bag. The mesh bag is awesome for dipping dirty dishes in the creek, lake, etc. to get large food gunk off before cleaning/sterilizing. Make sure you have one pot large enough to boil water in for sterilizing all the other pots/pans.
Oh, and get a GOOD air mattress and battery powered pump. Cheap air mattresses (walmart/target/academy house brands) WILL leak. You and your kids will be MUCH happier on an air mattress. Let the kids sleep one night on the ground and see how long they want to stay
Good luck! Camping is awesome fun.