Tent
Sleeping bags/duvet
Sleeping mats or airbed and pump.
Torch
Rucksack if you're not using your car as storage
Plastic bags
Food/water
Cutlery, plastic plates
Cooking equipment
A football, board games etc
First aid box
If you've never put up a tent before, put it up once or twice in your back garden as you don't want your wife and kids sitting their whilst you read the instructions.
To add to this (only?) helpful post (sorry for my lack of help)... Do you have any idea how much money you want to spend on equipment, and do you have any idea if this is something you'll do more than once?
There are lots of campsites and places to pitch a tent in this country. There is a very high percentage of those places that have nasty, 'orrible rocks where your back will end up on the floor. Air beds are great - invest in those. Or at least some good quality roll up mats... or thermarests

They're expenisve, but I find them better than an airbed, since they're lighter and you don't need a footpump (or some way of blowing them up, that you can't use your own breath for, e.g. car powered pump thing).
It's quite warm now, so you won't need super-warm 4 season sleeping bags. You could probably get away with 2 season ones, or 3 season ones. I have a nice sleeping bag, but I remember when I went camping with the parents when I was about 7 we just had very basic 80s sleeping bags, and an inner sheet thing - I was plenty warm in that, even on cold nights.
And that's in a draughty 70s tent.
I'm sure anything you can buy nowadays is way better, and probably has a fitted groundsheet to keep out drafts.
I'd take at least two torches... then the kids can have one, or as a backup. Spare batteries, maybe? They can live in the car (assuming you'll be in a car)
Plastic bags / bin liners - a MUST... if it's anything other than bone dry then things WILL get muddy and wet.
Foodwise - get a coolbox... most sites of any size will freeze ice packs for you, i've found. Get some spares for this purpose.
Camping is great fun, but you can make it a real camping experience, or just like being at home, but in a tent.
You may want to consider chairs and a table (the camping, folding variety) unless you want to sit on the floor to eat
