It really all depends on what you are looking for.
Hillman Ferry: Tourist camping but it has awesome facilities. (Clean bathrooms and shower stalls big enough for two if your wife is so inclined--just be prepared to be judged when you exit together). Outpost that rents bikes, dutch ovens, maybe a canoe, and has all the stuff that you either forgot or didn't know you needed. There are trails that surround that campground (1 goes to the rock quarry, 1 does a loop around the camp, and there is a spot to jump on the north/south trail about a mile outside the entry gate. The trail from Hillman back to the north welcome station is the best scenery of the entire trail IMO. Plus, there is a paved trail that will take you back to Hillman so you can loop it at about 5 miles if I remember correct. You can rent a boat at multiple places within 10 miles. Go to lake Hematite if you are looking for a good day trip with kids. Elk and Bison Prairie is 20 minutes south.
Back Country: I usually do my back country camping in the winter, but there are about a half dozen places you can go where you have access to water and a dry toilet. Most of them have a place you can launch a small fishing boat. You say you are going with your brothers, and if there are no women involved I would go this route. There are about 4 rangers in the entire park right now, so you can turn up the radio and pound some beers without any hassle. There is a quiet time at your main campgrounds that is enforced by grumpy old men who ain't gonna let you screw around on their watch. Smith Bay, Sugar Bay, and Birmingham Ferry are places I have spent many nights. If you have a good off road vehicle, hit a long gravel road and pitch a tent off the trail near the water. Make a big fire and empty a few bottles of bourbon. Just pick up a back country permit first just in case one of the rangers stumbles upon you.
Piney: The Hillman ferry of the South Entrance gate. Less tourist feel in my experience. More historic sites to visit, but you're in Tennessee and that place blows so I normally stay on the North end. There are cabins here that you can rent if you don't have an RV and don't want to sleep in a tent.