I'd choose music according to the Church's calendar: that is, according to which Sunday is being observed.
After all, the Mass for the ordination rite had readings and chants and music that referred to the priesthood. This Mass is different: it's a regular Sunday (or weekday) Mass. It doesn't have special readings assigned.
This is an opportunity for Father to say: I'm here to serve God and His Church. I identify with the Church, so I'm going to do what the Church's liturgy prescribes for the day.
Does Father feel comfortable in singing his basic parts ("The Lord be with you", etc.)? If I were choosing music for a priest's first Mass, I'd put all the emphasis on singing the Mass ordinary parts. That's the Church's goal. The Church wants us to sing the Mass texts, not hymns that are tacked on. It's the difference between "singing the Mass" and "singing at the Mass".
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