We camped in the State campground at Pettigrew State Park. It is a small campground with just a few camp sites. We usually overnight there on the way to the NPS campgrounds on the Outer Banks of North Carolina, though it is nice enough to justify a stay if you find yourself in the area. We visited in March, so insects were not a problem, though your experience may be different if you visit during the warmer months, as much of the area surrounding Lake Phelps is cypress swamp.
I little about the campground amenities: it is modest and good for tent camping. Though there is room for RVs, there aren't electrical and water hookups, though most who were there were in RVs. Each site has a fire ring with a grill and firewood is available for a nominal fee. There is a bathhouse with toilet and shower facilities.
The natural beauty is worth the visit. From the campground it is an easy walk to the lake. We were able to see an impressive sunset from the lake shore. There is an out and back 1.5 mile trail, for a total of 3 miles, that follows the lake, taking you through the Somerset Place State Historic Site. The walk passes through the swamp with many large cypress and sycamore trees. At the end of the trail is a walkway to the lake along an irrigation canal.