Hi Saprolith,
I would be inclined to buy as little as possible until you find that you need something... then go for it!
( its easy to get carried away and get lots of things that maybe you will never use and then they end up on Freecycle.)
To the stuff that has already been mentioned, you will also need a suitable waste pipe and connectors to join your grey water container to the caravan but hopefully the dealer will have done this for you.
You will need couple of pillows and sleeping bags, (but you will probably have these already) and a low wattage electric kettle is a handy thing to have.
A small supply of tea bags, coffee, sugar if required, can be decanted from your home supplies into suitable small containers that will be handy and save weight and space. Don't forget a spare loo roll...
You should be supplied with a "winding handle" in the kit Damian mentioned, so you can wind up the steadies when you leave home and hitch up .....You will also need it when you arrive on site to wind down the steadies.....
( take a tip from one who knows.... when winding up the steadies at home or at your storage prior to hitching up, never ever place the winding handle anywhere other than the front locker when you have finished with it, don't place it on the ground or propped up against a wall even for a second.... other wise like a lot of folks you will arrive at your destination, unhitch, and then find that the winding handle is safely propped up against a wall 50 miles away!) and that's not a good way to start your holiday!
As the weather is getting more chilly now, a couple of car rugs can provide extra warmth if the sleeping bags or other bed clothes, duvet etc., is too light for autumn or winter use.
Check you have a spare wheel both for caravan and towing vehicle, and a reliable tyre pressure gauge.....(and know the correct tyre pressures, and it's always a good idea to take a roll of duct tape a screwdriver or two and pliers etc. together with a "spare bulb kit" but you probably have one for the towing car anyway but check if you need any extras for the van. Its a good idea to make sure that your breakdown assistance package covers the caravan and your subscription has been paid.
Towing mirrors (both sides will usually be needed) as will a warning triangle ( there should be one in the towing car, but best to check) and also that the first aid kit, fire extinguisher, and smoke alarm is present and correct.
Unless you have a suitable electric cooking ring in your caravan or a microwave oven, its going to be difficult to use your cookware without having a gas cylinder on board... Propane is best for winter and is Ok for summer use as well, but butane works better in the summer and will not be much use in the winter at low temperatures.
Whatever you do, it's important you enjoy yourselves, don't take the breakdown/ tool advice as doom and gloom.... its a bit like insurance in a way.... if you have it then hopefully you will never need it, but if you do need it, you will be glad its there! :lol:
Best of luck with your new van
Regards
paws