Processionals/Recessionals
Jesu, Joy of Man’s Desiring (Johann Sebastian Bach)
Canon in D (Johann Pachelbel)
Rondeau in D (Jean-Joseph Mouret)
Air (G.F. Handel)
Air on the G String (Johann Sebastian Bach)
Ode to Joy (Ludwig van Beethoven)
Trumpet Voluntary (Jeremiah Clarke)
Trumpet Tune (Henry Purcell)
Sheep May Safely Graze (Johann Sebastian Bach)
Allegro maestoso (George Frideric Handel)
Alleluia (Wolfgang Amadeus Mozart)
These suggestions are simply a place to start. Other suggestions are welcome. Some selections feature recordings from the organ or piano. Either instrument will work for any of these pieces.
Hymns
All page references are Journey Song (piano or organ can be used for these).
Hear Us Now, Our God and Father p. 539
Where Love Is Found p. 543
Joyful, Joyful, We Adore You p. 575
Praise, My Soul, the King of Heaven p. 586
Lord of All Hopefulness p. 647
Love Divine, All Loves Excelling p. 709
Ubi Caritas p. 776
Taste and See p. 782
Entrance Antiphon
The Church has antiphons and verses for Entrance, Offertory, and Communion, which can be used instead of hymns or in addition to them. The Entrance Antiphon is a natural choice due to the timing of of bride and bridal party processions.
https://media.churchmusicassociation.org/books/sep/085_SEP_Nuptial-Mass.pdf
Other hymn suggestions are welcome.