You are on the right track by making most of your shifts using the right side. Think of the left side in terms of terrain: lowest gear (small front ring) for steep climbs; middle ring for easy hills and rolling terrain; and the big ring for flat, downhill, and gently rolling terrain. Since you don't want to cross-chain small-small and big-big rings, forget that it's 21 gear options. Keep it simple as you can go crazy trying to remember which gear combo comes next from any one position.
Enjoy your new bike!