I would buy a 6 berth tent with 2 (possibly 3) sleeping areas, an inside area and a porch. Think carefully about buying something bigger as it can be a PITA to fit in the car, put up, store, and then you buy tonnes of stuff to go in it.
I like thermal self inflating mats- lidl/aldi both do them as part of their specials but many shops stock them now at a reasonable price. Buy slightly better quality for the adults if you can as you are heavier and will notice the difference more.
You can take duvets/pillows from home (although I personally prefer sleeping bags). Buy a few cheap fleece blankets from Ikea or similar- nice to have on camping chairs, wrap up at night, sunshade, between the mattress etc.
Again you can take kitchen stuff from home, but look in wilcos/charity shops if you want to start a little collection to keep in a box. I prefer metal cutlery and melamine plates- makes it feel more like home. You will need sharp knives, bottle opener, chop board, plates, bowls, mugs, cutlery, fish slice, large spoon etc.
Think about how much cooking you are planning to do. If it's a lot, it's worth investing in a double burner or similar (or 2 smaller smaller laptop stoves but don't place them side by side). If you're planning to do breakfast and just eat out you might get by with 1 stove.
It's worth buying a small kettle. You will also need a water carrier (though we get a new 5 litre bottle from the supermarket every year and refill).
A few tables are handy, one high up for a 'kitchen' and a lower one. I prefer tables over clunky kitchen stands.
A cool box, or cool bag. You can get electric ones, but you can use frozen milk/blocks/prepared chilli etc to help.
EHU is a possibility, though watch out as some cheaper models have smaller length cables, it's worth getting a longer one.
Some way of lighting the tent- we just use cheap ikea lights, if you go non-EHU you will want effective battery ones.
The best thing is to just go and then nose around other people's set ups. Most campers will respond to a bit of flattery about their set up and are happy to justify talk about their purchases.
Just remember that more stuff isn't always a good idea!