Their music, not yours
The best choice is nearly always something that was theirs: the song they sang in the kitchen, the one from their wedding, the piece they played on a Sunday morning, the artist they never stopped going on about. It does not need to be sad. A tribute to someone who loved a particular band, played to that band, is often the moment in a funeral where people smile.
If nothing comes to mind, ask around. Someone will remember what was always on in the car. And if they had a favourite hymn, that answers the question on its own.
Think about the length
Most songs run three and a half to four and a half minutes, which suits somewhere between thirty and forty-five photographs. If you have a great many photographs to include, two songs back to back work well, and the change of music makes a natural chapter break — childhood in one, the later years in the other. A very long piece is worth a second thought: eight minutes of photographs is a long time in a crematorium, however loved the person was.
It is not a problem if the song is not quite the right length for the photographs. A good edit fits the pictures to the music, not the other way round, so a slightly short song simply means a slightly slower pace on each photograph.
Lyrics, or no lyrics
A song with words carries meaning, and if the words are right there is nothing better. But they need to be listened to right through first, because a chorus that feels perfect can sit above a verse that is about something else entirely. Instrumental music — a piano piece, a film theme, a classical adagio — asks less of the room and lets people look at the photographs without being told what to feel. Both are right; it depends on the person and on the family.
One song a service can carry
If the tribute is being played in the middle of a service, it is usually best if it is not the same song that will be sung or played elsewhere in the running order. A film set to the entrance music, followed twenty minutes later by the same music as the coffin leaves, loses something the second time. Check the running order with the celebrant or funeral director and give the film its own piece.
What happens with copyright
This is the part nobody explains, so here it is plainly. Recorded songs are protected by copyright, and a video editor is not licensed to build a commercial recording into a film and hand it over. What a crematorium, church or venue is licensed to do is play music during a service — they hold the licences for exactly that, and they do it many times a day.
So in practice a tribute video is edited to the exact timing of the chosen song, and on the day the venue's audio-visual team cues the recording alongside the film. It is how most services already run, it looks and sounds exactly the same to everyone in the room, and it means the film can be shared online afterwards without being muted or taken down. If a family wants a copy that carries its own soundtrack, the usual answer is a licensed piece from a music library, of which there are many beautiful ones.
Whatever you choose, tell the funeral director early. Some crematoria need the music requested through a particular service a few days ahead, and the last thing anyone wants is a film that runs in silence.