Playing the organ for a memorial service is about choosing music in consultation with the celebrant and the chorister, if there be one, that's suitable and sensitive for the occasion.
People in the audience sometimes struggle to sing at these events, many who attend may be overcome with emotion, and many may be unfamiliar, perhaps, with the hymns; this means that, if we're leading a hymn, we can't rely upon hearing people sing to tell ourselves which verse we're playing, so we have to make sure to count verses as we go.
It's important to remember that people are grieving during these occasions and need their spirits lifted ... gently, carefully, and thoughtfully.
Playing music in minor keys is too depressing; the opposite is also true: playing loud, jolly music may well be a bit insensitive.
The best kind of music to play at these times are pieces which are slow to medium in tempo and in major keys.
Hymns like "Holy God, We Praise Thy Name," "O God Our Help In Ages Past," or "Liebster Jesu," which are all in major keys, come out well played at a medium-slow tempo with a nice, warm flute or string tone just loud enough to help cover the sound of anyone who may be crying; other music might work better using an ensemble combination of flutes, strings, or maybe principal tone, provided it isn't too loud.
It's also important to remember not to be too thin-skinned and over-sensitive; the only person who has the right to criticize your playing is someone who plays better than you, and, if such a person is present, they will be full of encouragement for your efforts.
Just be sure you've prepared the music the best you can with the time you have available, and you can be prepared for people to come up to you afterwards, and thank you.