We're drifting from songs for a wake to songs for a funeral. Which is very logical, that's the right order to have thigs in. People sometimes talk about the party after a funeral as being a wake, but it's not, it's the night before, preferably in the locality of the deceased.

Funeral should have songs that represent what the person being buried or burned stood for, if they stood for anything.

So for example:
The Red Flag
The Strangest Dream
Faith of Our Fathers
Waltzing Matilda
Didn't he Ramble
Abide with Me (especially for football fans - that's "Soccer" to some people
Nearer my God to Thee (especially if you got drowned on a liner like the Titanic, or killed in a train crash like Engine 143)

Funerals tend to have much better songs than weddings. Good wakes are much more life enhancing than stag parties and hen nights. As I said "You can't beat death!"