Dont think you really can pick one core excercise?!?! Where's Bench in there?
Each hit a Anterior, Middle & Posterior deltoid different,..then ya got other parts that make up your deltoid chain as well...Pec major, Teres, Infra & Supraspinatus.
So for me my "Core" delt lifts would be; Bench, Up-right rows, and Rear Delt Cable Crossovers