Competition can be serious or just plain fun. Teens will learn a tremendous amount when forced to explain their reasoning and answers to their teammates. I teach handbells and recorders in a homeschool co-op. We borrow the bells from a church, which also donates practice space. We rehearse one to two times weekly, depending on our performing schedule.
Costs are very low.
Other successful group music activities include choir, band, even orchestra. Begin a band by employing private high school music teachers, whose schedules can usually accommodate homeschool groups that meet twice weekly. Listen to this homeschooling mother's description of science classes she organizes for teenagers in her area. I rotate biology, chemistry, physics and earth science each year. This year I had seventeen kids aged thirteen to eighteen.