Bishop Browning received his seminary education from the University of the South, commonly known as Sewanee. While there he was a member of the Phi Gamma Delta Fraternity. He earned a Bachelor of Arts in 1952, followed by the postgraduate Bachelor of Divinity in 1954. On July 2, 1954, he was ordained to the diaconate, and his ordination to the priesthood took place on May 23, 1955 in the Episcopal Diocese of West Texas. Browning was married to Patricia Alline Sparks on September 10, 1953. Together they had five children, Mark, Paige, Philip, Peter, and John.