A Composer’s Unique Selling Point
If you seriously want to pursue a career as fulltime composer, you should try to develop a strategy that sets you apart from the rest of the people in the business. The world doesn’t need yet another “media composer doing every sort of musical style”. Try to develop a special ability where you actually excel in to be able to compete on the market.
Your ultimate goal should be a reputation where people say “Oh, we need special skill X, I heard/saw composer Y is really good at that, let’s call him/her.” Actually shaping your career path like this is quite tricky at the beginning as you are rather thankful for every paid job that comes in, but the further you go the more often you might be able to actually pick more projects which sharpen your profile further.