One of the areas we have used that offers a bit of everything is Peck Ranch Conservation area in the Ozarks of Missouri. While it is not representative of all CA's, it does suggest what some of those that are most amenable to camping have to offer. There are two designated camping areas at Peck. One is designated for campers who will not use generators and one for those who will. This is nice for those tent campers who wish to have peace and solitude without the noisiness of a generator blaring in the background. At the non-generator site there are also pit toilets. Both campgrounds are outfitted with fire rings and picnic tables.
This is most certainly an example of a campground where there is much activity associated with deer and turkey hunting seasons. So, if you wish to avoid this, avoid visiting at these times. This unique CA has over 25,000 acres of total area, about half of which is a designated wildlife area and fenced off from the rest. It was once a logging operation and has some unique history as well as geographical features. Summertime is a great time to visit for those who are looking for a camping place away from the crowds.
Another example of a nice CA for camping at the other end of the state (northern Missouri) is Union Ridge just West of Kirksville. There, unlike most CA's, you can camp adjacent to area parking lots. Additionally, at "Parking Lot N" off of County Road D, there is a campground with similar facilities to those described at Peck Ranch. Again, things can be a bit hectic for non-hunters during deer season, but this area has more to offer than hunting. While not as big as Peck Ranch (around 8,000 acres), it has about 12 total acres of fishing lakes and ponds, including Union Ridge Lake. These lakes have populations of bass, crappie, catfish, and sunfish.
If you are camping at a CA, keep in mind that if there is a campground it will offer only "primitive camping" facilities. This means that you will have a fire ring, and perhaps a picnic table and/or outhouse. Having said this, some of these campgrounds are quite well maintained and in absolutely beautiful settings. Since some of these campgrounds are quite small, and there is no reservation system, you might wish to also be prepared to camp outside these areas.
If you choose to camp outside a campground at a CA, assuming this is allowed, keep in mind that you must be 100 yards from the nearest road or parking lot. Also, if you are camping along a stream or river, camp at least 100 feet away. Also, keep in mind that under certain weather conditions flooding or even flash flooding can be a danger.
To find a CA that meets your needs, a bit of research can go a long way. Fortunately, there is a very nice resource to aid you in this process.