Camping your first time can be scary to prepare for, but with a few tips, trial and error on what works for you and your family, it can be pretty easy.
I am going to make some recommendations here for the Scouting family that believes they will be an active participant and eventually transition from Cub Scouts to boy Scouts. Also, my goals will be to minimize cost and minimize redundant gear across multiple use cases. The recommendations will suggest better gear that will last a little longer.
Tent: 6+ person tent = $150 - $500 or 4 person tent = $50 - $150
Lighting: Headlamps and Lightweight lantern = $10 - $50
Sleeping bag: 2 lbs + 20 degree + synthetic or water-resistant down filling = $100 - $400
Sleeping bag liner: 8 oz. = $25 - $60
Chair: 2 lbs Backpacking chair = $30 - $150
Table: Any folding table that fits in your car = $30 - $250
Mess kit: lightweight cup + Sea-To-Summit Summit bowl XL + GSI Outdoors Spoon + any Fork = $40
Knife: Multitool = $40 - $100
Bottles: 1 Liter + BPA Free plastic = $8 - $20
Cooking:
Stove 8000 BTU
3-5 Liter pot
Frying pan
Spatula
Serving Spoon
Cutting board
Kitchen knife
Cleaning
Bleach - for 3rd step of KP
Dish soap - for 2nd step of KP
3 wash buckets for steps 1-3 of KP
Sponge
Drying rags
Tent: 2 lbs + 3 season = $100 - $300
Lighting: Headlamps and Lightweight lantern = $10 - $150
Sleeping bag: 2 lbs +20 degree + synthetic or water resistant down filling = $100 - $400
Sleeping pad: 1 lbs + Insulated = $50 - $200
Stove: Jetboil(only 1 needed per 4 people) = $79 - $180
Mess kit: light weight cup + Sea-To-Summit Summit bowl XL + GSI Outdoors Spoon + any Fork = $40
Knife: 2-3 inch jack knife + light weight = $15 - $50
Bottles: 1 Liter + BPA Free plastic = $8 - $20
Backpack: 75Liter(Scouts)/85Liter(Adults) = $150 - $450
Unfortunately, there probably isn't one size fits all. I have a tent for the Family(of four), a 2lbs backpacking tent, and a 2 man tent for myself when car camping with Boy Scouts. I will identify Tent by the situation. If you are on a budget splurge on the lightweight backpacking tent(around $200) and go budget on the other tents.
Cub Scout Family Camping (2 adults + 2 kids) - Get a tent that you can stand up in and have room for gear. So get 1 or 2 sizes bigger than the number of people. So if you have 4 people get a 5 or 6 man tent. Expect to pay $150+ at Big 5 and Walmart and more anywhere else. I use this tent the least. With a bigger tent come other things that you will need:
Doormat to leave your shoes on and wipe off dust
Brush and Dustpan
Cots or Queen size mattress
Tent footprint.
Bear to Arrow of Light and Boy Scout camping(1 adult + 1 kid): Our Boy Scout troop provides tents for the Scouts but not the adults. Boy Scouts and Adults should not share a tent. So Boy Scout adults need their own tent. Our Cub Scout Pack does not provide tents. Cub Scouts sleep with their parents. This tent should fit both roles and be small enough to carry several hundred yards. A 4 person tent is ideal for this type of camping. It will just barely fit a queen size mattress. You should be paying $50+ for this tent.
BSA will have two types of campouts, some that require moving gear from transportation to campsite is under half a mile(car camping) and some that require that you will carry all of your gear on your back(backpacking). New BSA Scouts they will spend the first few years mostly car camping. My suggestion is that new scouts get gear that they can make mistakes with. When they start backpacking they will get much higher-end gear. For beginner car type camping, I recommend the following mandatory gear:
Sleeping bag: 20-degree rating, 4 lbs, around a cubic foot in size(or smaller), under $90.Sleeping pad with an R-value(thermal resistance) rating.
The folding foam type is 10x faster to setup and put away than an inflatable. Under $60
Wide mouth Nalgene brand water bottle. It will last forever and is compatible with our water filters. Under $15
Duffle bag with removable shoulder strap. It should be big enough to hold 3-4 sleeping bags(from above). Under $40
Hiking boots: Should be ankle height, and water-resistant is preferred. At this age, their feet grow very fast with this in mind buy boots believing that they will only last 6 months.