I have a feeling that Sweeney will do The Ballad. It's the opening number, so it doesn't give anything any plot and it's an ensemble number. Even though only three cast members are nominated, this version of Sweeney truly is an ensemble show and I think that the producers will want to put the focus on the ensemble.
If they decided to do something else, I think that Good, That's Good is the best choice- all three nominated actors are in it and everyone else is still in the scene as customers. I really don't want to see a shorted verison of A Little Priest.
There's a lot I am not certain of...