If the base campground on the beach doesn't work out, within your criteria you also would find the Croatan National Forest Cedar Point, NC Campground. It is about a 20 minute drive from the Route 24 main gate of Lejeune.
Cedar Point is inexpensive (honors the senior pass for a discount but can be reserved ahead) and has electric hookups. Shady, quiet, has boat launch, walking trail and bathrooms with showers. Just stayed there last weekend for the second time. Good grocery store, gas stations, fresh produce at farmers markets etc. nearby.
The NF campground is a few miles from the intersection of 24 and 58. 58 is the bridge over to Emerald Isle beach community. Very short ride to beautiful Atlantic Ocean beach and lots of restaurants.