Short, basic answer...Alternative or Punk Rock with a horn section. Some bands you may want to check out for familiarization with the genre: Reel Big Fish, The Specials, The Aquabats (reputed LDS, BTW), The Might Might Bosstones, and Save Ferris (a personal fav) just to name a few. Learn to skank dance and you'll be the coolest kid in the hizzo.
For a more historical view ask Faerie...she's down.
Therefore, since Moroni is rockin' the trumpet...Moroni Plays Ska.