Pest Control: Don’t Skimp! Use the best mouse traps money can buy. The linked site shows the best options for your camping needs.
Storage Equipment: Some form of collapsible chuck box is necessary to keep all your camping gear together and store loose items. A cooler box or bag is a necessity for camping and keeps foodstuffs fresh and clean. There are various types available, but if you are using one hat is connected into your vehicle power supply, then ensure it does not discharge your vehicle battery fully. I prefer to power the camping cooler box from a booster pack to avoid this risk. If you are on a serviced site , they will generally have a freezer to enable you to refreeze ice pack, have a double supply and you can keep the cooler box cool at all times. Ensure they are marked so that they are identifiable from other campers ice packs.
Water Container: A water container capable of holding at least 5 gallons/ 20 litres is essential, this will enable cooking etc to occur with the need to run for additional water.Collapsible type camping water containers are generally good quality and do not take up much space.
First Aid kit: A good first aid kit is essential and you may already have one in your family vehicle, if not do yourself a favour and purchase one now. In addition have a small pouch type first aid kit for when you are away from your camp partaking in activities. Additionally ensure you have adequate sun cream, insect repellant. Insects can be a bit of a nuisance on some campsites.
Camping Lanterns.: You probably have one good quality light in your family vehicle, in addition to this equip each member of your family with a reasonable quality camping head light, led type with rechargeable batteries, keep them all the same and have additional charged batteries.
Multi tool: Bring a reasonable quality multi tool as part of your camping gear so that you can cope with the small tasks around your camp.
Eating and seating : You may want to bring a collapsible picnic table and camping chairs or you may be going on to a serviced site that have adequate benches and seating areas already. Personally all I would bring is a couple of waterproof backed picnic blankets, roll one of these out anywhere on your camping trip and you can relax, sunbathe or set it up to have your food.Wind breaker. A wind break can have two functions, the obvious main one is to protect your camp from gusting wind, but additionally it improves your privacy somewhat. A couple of 12 foot windbreaks complete with poles is not very bulky and you can also use it to air wet towels if you are swimming etc.
Hopefully the above covers the basics and you will have your own camping checklist. Your list will reflect your families interests and the activities you wish to undertake whilst camping. If you need additional camping gear, then Amazon has a great choice and you can get discounted prices regularly.