Lots of websites will suggest hymns which are appropriate for a wedding ceremony, and if you, your fiancé(e), and the majority of the guests, are church-goers, I suggest you look at one of these websites. A Google search will bring up the latest.
However, at the majority of weddings, church-goers are not even close to being in the majority. The singing of hymns breaks up an otherwise wordy service and allows for real participation in the celebration by your guests. So pick hymns you and your guests will know, so you can get the most enjoyment out of singing!
There is a really good collection of popular hymns which has been produced by BBC Songs of Praise: https://www.bbc.co.uk/programmes/articles/103B6cz62PRtwndg0FbwBxh/hymns-for-weddings
In church weddings, you will need to go to a side-chapel or vestry to sign the civil paperwork. This is often an opportunity for official photographs to be taken, and usually comes very shortly before the end of the whole ceremony.
During this time, which is generally between five to ten minutes, it is usual to have music played. If you have a guest who is particularly musically talented, this is the best point to have them perform something especially for you. If they need accompaniment, I’m happy to provide it, and if they only need rehearsal on the day shortly before the wedding, this is free of charge. I can only accompany on instruments available in the church, which is almost always an organ and often a piano too.
If you don’t have a guest who is willing and able to perform, I can play throughout the signing of the register. Most couples tend not to have particular items they want to have played at this point, or perhaps just one, and so I am happy to just get on and play some of the items listed below. But I’m also delighted when couples do want to programme this part of the service. I like a challenge!