Tom Kelly's guide book "The Climber's Guide to North Carolina" covers Stone Mountain as well as other areas.
Classic route: The Arch (5.5). Takes gear and is more like routes in other areas.
Most Stone Mountain routes have long runouts between the bolts with little or no chance to place your own pro. Many routes offer the opportunity to break your ankles if you fall before reaching the first bolt, often 30'+ off the ground.
Start by doing "U Slot" (5.7) off the ground to reach Tree Ledge from where many of the good routes begin. U Slot has the advantage that it starts out as a normal trad route, protectable easily in the dihederal for the first 40' After that, relatively easy friction section with almost no pro until you reach a roof (ceiling?). Pulling the roof is the crux, but you can protect it with cams in a crack below the roof. Note that if you have a 50m rope, your belayer needs to be right next to the start of the route, and you'll still just barely make it to the tree where you can set up an anchor.
After U-Slot, try Yardarm (5.8-) to get a taste of "real" Stone Mountain climbing.
After Yardarm, up the ante a bit by doing Mercury's Lead (5.9-).
An excellent route that offers more traditional climbing on the first pitch is "Fantastic" (5.9). The second and third pitches are typical Stone Mtn slabs with long runouts.