They'd probably enjoy classical, opera and all generes related to power metal (speed metal, nu metal, neoclassical metal, opera metal, heavy mithril, dwarf metal, etc).
If they were to listen to our music, they probably would be fans of 70s hard rock, as that was when they were in school. Sirius was in Azkaban from 1981-1993, and then was a fugitive for another two years, so he wouldn't have had much knowledge of 80s and 90s music. Classical seems like a good fit for Lupin.
