Okay, some people have been having trouble with their characters not appearing. They will join the game and appear as Marcus Fenix instead. After about 30 minutes of starting and quitting to get our characters right, to no avail, we found that if you JUST DIE AND RESTART AT WAVE 1, your characters should respawn as the character you chose before the match.
Just wanted to throw that out there in case anybody was confused by this like we were ;)