I worked in music administration for about a decade so I can just share some information about the career paths I've seen students and alumni embarking on:
Roughly 60% go into teaching
About 15% end up in music or general administration
10% become performers or composers. These would be the students who are the cream of the crop, as you already know that available positions in orchestras and ensembles don't open up every day
The remaining 15% do something unrelated to music
I found that the most successful graduates usually straddle two or more of the categories. To make a living as a musician, it's probably necessary to wear many hats unless you're one of the lucky few who get to audition for the Berliner Philharmoniker.
For composition majors, I've seen a few of them become successful conductors. One guy I know built a great network and gets regularly commissioned to compose pieces for national performances. He's definitely an anomaly, though.
Are you from Juilliard or Berklee? If you're from one of these two, you will definitely have a significantly easier time finding work.