The most renowned composers currently in Oxford are Robert Saxton (Worcester, leaving shortly) John Traill (St. Anne's) and Martyn Harry (St. Anne's, St. Hilda's), and there are plenty of others.
For a moderate amount of choral singing, avoid the choral foundations (Christ Church, Magdalen and New). Queen's and Merton are the best mixed-voice college choirs in Oxford and sing 3 services/week. Worcester, Somerville, Exeter et al. are fine; avoid Trinity, Lincoln, St. Edmund's, Brasenose and St. John's. When (if) you get to Oxford, consider auditioning for Schola Cantorum in Freshers' Week. There are several a capella groups as well, if you're into that.
I'm not a composer, but I understand that composing at Oxford tends to happen at the university level, rather than the college level: some people who take composition for Prelims (1st year) and finals have tutors from different colleges, and composition competitions (by colleges, the Faculty, OUMS etc.) are open to everyone regardless of college.
You apply for a choral award by filling in this form
https://www.ox.ac.uk/admissions/undergraduate/applying-to-oxford/choral-award-application-form by 1 September and fulfilling the other requirements detailed there. You attend auditions at your chosen college in mid-September. You are then expected to apply through UCAS to the college which offered you a place in their choir. You may be pooled to a different college when (if) you are made an offer; this is one of the ways in which you can sing and study at two different colleges. If you want to, you can try emailing your pooled college to ask to audition there instead, but this is subject to availability/whether they want you.