Possibly "Go, Ye Messengers of Glory" & "Go, Ye Messengers of Heaven"
Photo from history.lds.org
While history has not recorded President John Taylor's favorite hymn, it does note he was well-known for his singing voice and love of music. In fact, he wrote the lyrics to two of today's current hymns: "Go, Ye Messengers of Glory" and "Go, Ye Messengers of Heaven."
These two hymns both reflect President Taylor's fervor for missionary work. At the time he penned them, he was serving as a missionary in Britain. His efforts there would bring thousands of souls to a knowledge of the truth.
Later, President Taylor also served as an editor for the 1840 hymnal, and he likely enjoyed much of the music included therein.
Learn more in Our Latter-day Hymns: The Stories and the Messages.