Just been through our kit list...
Sleeping... we take SIMs now but started out with airbeds which were fine for a few nights and come in handy for sleepovers etc. as DC get older. Sleeping bags - the best you can afford (and again, used for school trips, sleepovers). We take our own pillows and a couple of fleecy blankets just in case. Picnic rugs are great to go under the airbeds and provide some insulation (www.gooutdoors.co.uk/freedom-trail-fleece-picnic-rug-p362064). They also make a good carpet and make the tent feel warmer for sitting in the evenings.
Sitting... a couple of tables and, if you can, get some better quality chairs than the £5 ones that you find in Tesco.
Cooking... we've experimented with lots of stoves but keep coming back to the briefcase style ones. Don't forget spare gas canisters. Pans from home will be fine, don't forget a frying pan for breakfasts. If you have EHU then a cheap kettle is worth taking. Check whether the campsite has facilities for freezing ice packs for a cool box- if so, take spares so that some can be freezing overnight while the others are in the cool box. Freeze milk before for go (and wine bags) as they will defrost gently.
Think about what you might cook. For a long weekend we might take a chilli that just needs heating (and have with crusty bread, tortilla chips etc rather than cooking rice). A disposable barbecue might be an option for one night to do burgers/sausages and then sandwiches/pub lunch means that you only need cooking stuff for breakfast.
We buy one of the big 5l bottles of water to take with us and then refill as needed.
Plates, cutlery, mugs, plastic glasses. A wooden spoon, tongs for bacon etc, fish slice if you might do fried eggs, big plastic spoon.
Pack a sharp knife, scissors, matches, baby wipes. Washing up bowl and 'washing up kit', 'Dettol wipes' or equivalent for tables. Kitchen roll, tea towels, pegs, spare toilet roll, citronella candles for sitting outside.
I have a list of all of the essential kitchen stuff that I know we take every time - teabags, coffee, hot chocolate sachets, salt/pepper, cooking oil, brown sauce, butter, milk etc.
Lights, torches, headlamps for DC are popular.
'Travel Johns' are handy to avoid having to go to the toilet block in the night but let the DC practice at home first...
First aid kit, chargers, spare batteries. Flip flops for the shower. Microfibre towels are also handy. A washbag with a hook is good to hang on the door for showers and stops everything getting wet. We take stuff to the shower in the big supermarket bags, again so that you can hang them up and keep things dry.
Sorry this is so long, hope it helps a bit. Have fun!