The parish where you are getting married should provide guidance on this, such as a list of hymns, or a book where you can choose hymns.
Parishes also have guidelines on what you are allowed to use for processional and recessional. My parish for example allowed the Wagner “Lohengrin” music (“Here Comes the Bride”). I understand some parishes do not.
I know one piece that was often used at parishes where they didn’t allow “Here Come the Bride” or the couple didn’t want that, is Purcell’s “Trumpet Voluntary”. However, your parish would need to allow it and you would need to have an instrument (trumpet or organ) capable of playing it.