Capt. Stockton enlisted in the U.S. Navy as a Cryptologist in 1990. After three years of service and four years of Naval ROTC, he graduated in 1997 from Jacksonville University with a Bachelor of Science in Philosophy and received his commission as an Ensign. He initially served as a Surface Warfare Officer and then redesignated as a Human Resources (HR) Officer. Stockton graduated from the Naval Postgraduate School in Monterey, California, with a Master of Science in Manpower Systems Analysis.

At sea, he served aboard USS Heron (MHC 52), earning the Commander, Mine Countermeasures Squadron 1 Shiphandler of the Year award. After learning about the Aegis combat system aboard USS Carney (DDG 64), he was assigned as the training officer and anti-air warfare coordinator; in the aftermath of Sept. 11, 2001, the Carney supported Operation Noble Eagle as part of the John F. Kennedy Carrier Strike Group.

His shore tours include service with Afloat Training Group Mayport as a training liaison officer; Naval Station Mayport, Florida as the administration department head (N1); the staff of the Military Personnel Plans and Policy Division (N13), Office of the Chief of Naval Operations, in Washington, D.C., as the officer accession planner; U.S. Naval Forces Central Command Forward Iraq as Assistant Officer in Charge during Operation Iraqi Freedom and the transition to Operation New Dawn; and the U.S. Navy Element at U.S. Southern Command as Executive Officer, focusing on expanding the global special operations forces network. In April 2014, Stockton became the twenty-first Commanding Officer of Naval Technical Training Center Meridian, Mississippi. At Navy Personnel Command, he served in the HR Community Management/Assignment Branch (PERS-4421) as the HR detailer and then as Deputy Division Director for officer detailing for staff/restricted line (PERS-44). Stockton was the Director for Total Force Manpower/Manning and Civilian Human Resources Directorate (N1) for Naval Education and Training Command, supporting the MyNavy HR Force Development domain. In 2021, he assumed the duties as Commanding Officer, Center for Service Support, Newport, Rhode Island. In 2023, he assumed the duties of Officer in Charge, Navy Recruiting Orientation Unit, Pensacola, Florida.

Personal awards include the Bronze Star, Defense Meritorious Service Medal, Meritorious Service Medal (two awards), Navy and Marine Corps Commendation Medal (two awards), Navy and Marine Corps Achievement Medal (three awards), Army Achievement Medal, and various unit, campaign and service awards. He is a joint qualified officer and certified as a Professional in Human Resources.