The trade off of most camping gear is cost vs weight vs quality. Car camping gets the "weight" issue covered. The only time I buy higher end gear is for HIKING type camping and need to shed weight. Mostly I stick with the Ozark Trail or Colman stuff. It is affordable and easily replaced.
Before you go be sure to set everything up in your back yard, make sure it is working and all there. This gives you a chance to try everything out so you aren't figuring it out for the first time on site. On a similar note, don't worry about how it looks when you break it all down to come home, because you should set it all back up again to get it aired out and cleaned before you roll it up right for storage.
TENT
Any of the Wal-mart 6-8 person tents will do you right for 2 adults and 2 kids. A lot of new ones even have a divider. I'd not separate from the kids the first few times if you think they will be scared, because they will just end up back in the "grown ups" tent anyway. These family style tents are roomy and have a lot of mesh for air flow, but are only reliable in fair weather, even with the rain fly. Costs new....$50-80 or so.
SLEEPING
Same as above, fair weather bags are good down to 40F or so, and can be had new for $20 each. I prefer these to be bought new, just like I wouldn't by used linens for my bed at home

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WATER
Any national or state parks will list if they have services like water or electric availabe on kept/numbered camping spots. If they do, great, you can get a couple of jugs to use to make koolaid or tea, your set. Otherwise, you have to consider it a necessity. Even if water is available from a spigot, you should have a case of water, just in case.
STOVE
Propane is by far the easiest way to go, just like using gas at home. Fuel is cheap and readily available. If you think you need two portable tanks, bring three. Try to stick with food that is easy and quick to heat. For instance, if you want mac and cheese, a kid favorite, get the single serving kind, rather than a big box you make. Less mess to clean up, and you are only having to boil the water. Hotdogs and burgers can typically be cooked over the fire.
DISHES
Paper/plastic products all the way. When done, dump them right into the fire, your dishes are done. I always bring a bucket of some sort. Use it for quick hand washes, etc etc. Handy to have a bucket around. Ziploc bags are handy too.
LIGHTS
Everyone gets a cheap $3 LED flashlight to call thier own. A good two mantle propane lantern will be plenty bright for the campsite. LED is the way to go here for anything battery operated. Brighter, easier on batteries. Remember you'll get some light from the fire too.
SEATING and COMFORT
The older I get, the more this means to me. I like my zero gravity chair. I used to sit on an unsplit log and be fine. I also used to sleep on the ground, now I go air matress. All depends on your tolerance. Air Matresses can keep you warmer too, providing a barrier between you and the cold hard ground. Most sites have a picinic table. A folding card table is good to have. Got a truck? Tailgates work great too.
SHOWERING
Like water and electric. A lot of state parks have showers. You usually pay more for a site if they are available. If you are going for just the weekend, shower when you get home. I camp near streams and rivers almost exclusively. I have been known to put on my swim trunks and grab a bar of soap and wade in

.....trunks are even optional! lol