J.B.
There are many different types of places to camp. Since you're a novice, you should probably try some state or national park areas first (we aren't novices and still love those areas with kids!) -Usually you'll have a bath house/flushing toilet somewhere and a water source. You should always plan to bring plenty of drinking water in case the water source at your campsite or at the park isn't potable.
Most park camping sites have grills or grill areas for your use as well. There are tons of new "portable" grills at appliance centers these days for tailgating and camping, and you can always get a hibachi.
We like to find state parks with swimmable lakes/beach areas during the summer. Usually there is hiking and often you can also rent boats, canoes, paddle boats, etc. Depending on the park there may be fishing, tubing, miniature golf, horseback riding, tennis -some even have pools and offer summer concert series. Take some games and bikes. Often a state park or national park will be near some type of attraction you can visit as well.
I recommend a NICE air mattress for the adults! We have a queen-sized one that cost about $100 at REI, and it has lasted 10 years! It holds the air, so you don't wake up on the hard ground. Your 4 year old would probably love one of the air mattress/sleeping bag combos you can find very cheaply at Target or Walmart. My 4 year old has a Lightening McQueen one that's actually been pretty durable.
Take plenty of wet wipes, paper towels, real towels and bug spray. Take citronella candles and something to build a campfire with. Take lanterns -battery or gas powered and a camp stove (I still love the classic Coleman you use the gas canisters with). Nothing is better than breakfast outside from the camp stove! If you have to have coffee, there are Lexan French presses available online and at REI. I think I saw one at Target too. When car-camping I like to throw in sheets, a blanket and our pillows -I mean -why not?
As far as a tent -I've had ultra expensive backpacking tents, medium range, etc. The best family tent we've ever had is a 3 room Eddie Bauer tent I got on clearance from Target for $27. As far as tents go -Coleman won't steer you wrong. If you want a little more high-end -go to REI. My rule for festival and other car-camping events though is to have a tent with a center clearance of 6' so my husband and I can stand upright in it. It may seem like a small thing -but it makes you so much more comfortable!
Here's a list of must haves. I camp a lot and now I'm camping with a 19m old and a 4 year old. We go to state parks, music festivals -wherever:
*Bug spray/mosquito repellant
*Citronella candles in the buckets
*Lanterns/flashlights -head lamps are AWESOME for night maneuvers -especially if there's a port-a-potty situation involved
*Comfortable air mattresses and pillows. Invest some money in a high quality air mattress -you won't be sorry!
*A few tarps for ground cover under the tent or to tie at a slant above the tent for rain cover/shade.
*Cooler full of food and favorite drinks
*Plenty of drinkable water -we get the 2.5 gallon containers.
*Sunscreen
*First Aid kit -band aids, itch cream, antiseptic wipes, neosporin, alcohol, gauze and tape, one of those cool/hot packs
*Something to start fire with -preferably a lighter (and for campfires -wood,kindling, etc.)
*Camp chairs -the kind that fold up and usually come in a bag for easy transportation.
*Usually state parks have picnic tables on site, but bringing a folding camp table is never a terrible idea.
*Trash bags, paper plates, cups, utensils, gallon zip-locks
*Duct tape, rope, utility knife or Leatherman tool, can opener
*Dr. Bronners or other environmentally friendly soap. Dr. Bronner's can be used to bathe with, wash dishes with -whatever.
After the necessities -it's up to you!