Who picks the music at Mass varies from place to place. In some parishes, there is a special liturgy committee that helps select the music for worship. In other parishes, the responsibility is left up to the music director. Almost always, the pastor has at least some input on what music is sung at the Mass. If you are interested in finding out how it is done at your Church, just ask the pastor or music director- they should be able to answer your question. For more information on how music is selected see here.