These are some of our camping hacks
2 or 3 35 l Really Useful boxes - totally bug proof for food, stable enough to double up as a kids seat or wine glass table. Fidgety kids much less likely to fall off them and spill cornflakes all over tent. Then you can keep your camping stuff pre packed in them between trips.
We have one of those roll out tables like this, you can get them everywhere, we cut about 4 inches off the table legs (so you can still fold it up) so its a better height when using this kind of arm chair. (see comment above re children and cereal). I would not buy children's chairs, they will just want to sit in your decent chair instead!
We have one lantern for the tent and a head torch each. We just use bags-for-life for organising stuff.
Good for washing up bowl
Buy a 5litre mineral water with a little carry handle and then refill for your water container during your stay.
Always take something for clothes line and few pegs even just to dry towels after shower.
It's a real balance between taking enough stuff to be comfortable and having so much that packing the car and setting up/striking camp become a PITA that takes the fun out of the holiday. People range from completely minimalist to home-from-home with rugs and fruit bowls.
We use thick mummy sleeping bags and self inflating mats to keep the pack space down, do take decent pillows. Your sleeping bag should have a "comfort temperature" of close to zero or be 3-4 season, if it doesn't quote either it will be a rubbish sleeping bag. If you go for airbeds you will need a thick blanket under you to insulate. Some people take loads of duvets but depends on space I guess.
Worth getting familiar with Decathlon and Go Outdoors or your local camping shop and THIS WEEK in Aldi - sleeping bags and mattresses. Including a camp bed which with a SIM on top could be an excellent bed.
Start with a short break to test your set up - maybe even near home so you can visit first. Also look at UKcampsite website for campsite and tent reviews.
Worth having a small, sturdy table for your cooker, secure it with a couple of tent pegs, and as stated have a windbreak around it. Does your tent have a porch? Then you can put bunting round and other MNers will recognise you!