My very first overnight self-supported cycling trip was to Jordan Lake in July of 2013. We road 60 miles in the heat to Crosswinds Campground with over 2000 feet of climbing and averaged over 13 miles per hour with our loaded bikes. It took over 4 hours, with breaks along the way for lunch and snacks.
I would recommend a road bike or touring bike with Bontrager AW3 28c or wider tires that provide puncture resistance with some light tread. It is good to have multiple bottle cages for extra water in hot months. The bike will need light-weight rack and panniers and various bags to accommodate all required gear for an overnight trip (tent, food, stove, and clothes), front and rear lights for riding on the road and standard repair kit. This was our first big trip, so of course we over packed.
It was nice to enjoy all the amenities of the campground. Went for a swim in the lake. Took a hot shower in the bathhouse. Used the picnic table to cook and eat dinner. Restrooms available as well as trash cans. Luxury, sort of.
Return trip was slightly longer but less hilly route of 64 miles and took us almost 5 hours. We were beat from the first day, but still had to get home. Planning and patience made our first experience of bikepacking a success. The extremely heavy bikes made us rethink a lot of our gear choices.
For more information on camping at Jordan Lake checkout www.ncparks.gov/jordan-lake-state-recreation-area