I have never thought about what I’d want for sacred music at my funeral until now, even though I sing for funerals all the time.
For me, if my family can’t hire competant musicians, I would prefer no music at all except to have someone chant the psalm, Gospel Acclamation and to have chanting for the parts of the mass. (I really don’t like most of the settings to the mass now-a-days. Some are ok, but there is one which I and many of my colleagues from various parishes or just my Catholic musician colleagues in general cannot stand. Thank goodness we don’t do it at our parish. I won’t say what it is, but we have a nickname for it, calling it the mass of destruction.)
If competant musicians could be hired for my funeral, I would want some movements of the Requiem mass by Maurice Durufle for organ and choir. I believe that the church no longer does Requiem masses (Why is that? They seem to be more meaningful. If they still did Requiem masses, this would be the mass setting) I’d want the Pie Jesu from that Requiem sung for my sending off at the end of the mass. I know, this is just an ideal. Durufle really knew how to incorporate the chants beautifully and perfectly into his compositions and still be extremely reverent with it.
I also love the Faure Requiem Mass (it’s an extremely close second), but the Durufle is my favorite.