Is there music at each Sunday Mass? Is there a Mass where a full choir sings works of sacred music?

The main choir typically sings at the 10:30 Mass, although they might be off for the summer. There is usually a choir and quartet at the 6:30 pm Mass on Sunday, but it's more contemporary than what you're probably looking for. There are also free Bosetti Concerts which typically showcase sacred music. You can check the website for the schedule of those.

I do not attend the Basilica regularly, but every Sunday Mass i have attended there has been a lovely choir and beautiful sacred music.