Airbeds are a good choice for your first camping trips - not too expensive and you can always upgrade to self-inflating mats later. However, ALWAYS put something more than a sheet between you and the airbed - the air in the bed gets very cold from the ground so you need a fleece blanket or an open sleeping bag under you. A duvet over you is a good and cosy option if you have space in the car.
Tent-wise, if you don't need masses of space, a pop up family tent from Decathlon is a good option. They are really easy to put up once you get the knack and there are online videos to help. Saves spending half an hour or longer putting your tent up when you arrive on the site - you can crack open the wine much earlier on!
We have a 5m bell tent - they look great and are also very quick to put up - stick up the centre pole, peg the guys out and off you go. However, they only really appeal if you are into open-plan living, although you can get inner tents for them now.
For cooking, I think it is worth bringing at least a small camp stove like this:
www.ebay.co.uk/itm/PORTABLE-GAS-STOVE-COOKER-CAMPING-FISHING-BARBEQUES-ETC-/180841716049?_trksid=p4340.m185&_trkparms=algo%3DDLSL%252BSIC.NPJS%26its%3DI%26itu%3DUCI%252BUA%26otn%3D10%26pmod%3D130616341646%252B130616341646%26po%3D%26ps%3D63%26clkid%3D7317682957522994403
or this if you want something a bit bigger:
www.homebase.co.uk/webapp/wcs/stores/servlet/ProductDisplay?langId=110&storeId=10151&partNumber=3402021&c_4=4%7Ccat_14419397%7CCamping+Stoves+and+Cooking+Accessories%7C14419406&c_3=3%7Ccat_26036006%7CCamping+and+Caravanning%7C14419397&c_2=2%7Ccat_16849255%7CCar+and+Travel%7C26036006&c_1=1%7Ccategory_root%7CGarden+and+Outdoors%7C16849255&&cmpid=AFPFD&_$ja=tsid:18771
You will also need fold up chairs of some sort unless you like sitting on the ground and lots of warm clothes and layers for the evenings which can get quite chilly even in summer. Choosing a site near a pub or which allows open fires is a good idea so you can keep warm (and cook marshmallows too in the case of the fire).
A coolbox for milk, wine and beer is also essential even if you are planning to mainly eat out. It is also nice to be able to have a cup of tea in the morning so tea, sugar and plastic/enamel mugs are also a good idea at the very least.
Most of the rest you can build up after your first trip when you have a better idea of the sort of camper you are and what equipment would suit you best.
Oh and bring a good torch for everyone and a lantern of some sort to light the tent. Campinggaz do good gas lanterns - I wouldn't use one of those if you have small children though as you don't want to risk them knocking them over. A battery powered one would be better in that situation - we have one like this but you can get all sorts of different ones from places like Millets, Robert Dyas etc:
www.decathlon.co.uk/11-w-neon-rechargeable-lantern-id_8090100.html
Anyway, whatever you decide have a wonderful time!