You could always use the Entrance Antiphon (Introit) from the Propers. However, if you want to use an entrance hymn, instead, then personally, I would choose something traditional, such as “Praise My Soul, the King of Heaven,” or “O God Beyond All Praising.”
For the offertory hymn, I would use either “Love Divine, All Loves Excelling (If you do not use “Alleluia, Sing to Jesus,” as the Communion hymn, but this could work as the entrance hymn, instead),” or “Lord of All Hopefulness/Be Thou My Vision.”
For Communion, I’d use the Communion Antiphon from the Propers, but if I had to select a hymn, then I would choose either “Alleluia, Sing to Jesus (if you didn’t use “Love Divine, All Loves Excelling,” as either the entrance hymn or the offertory hymn),” or “Let All Mortal Flesh Keep Silence.”
For the recessional hymn, again, I’d choose a traditional hymn, such as “Holy God, We Praise Thy Name,” or “O God, Our Help in Ages Past.”
As for a Mass Setting, any of Steven Janco’s Mass Settings (Mass of Wisdom, Mass of Angels and Saints, and Mass of Redemption) are great. Do NOT use Mass of Glory, Mass of Christ the Savior, or Mass of St. Ann. Use Missa de Angelis, if you really want to up the traditional, though.
Stay away from the Haugen/Haas/Schutte nonsense.
Let’s be honest, though. “Here Comes the Bride,” “Canon in D,” and Mendelssohn’s Wedding March are cliche/unoriginal.