I haven't played republic yet, but a lot of the Empire world arcs are some commander being terrible and you doing his job for him. A few do stand out however.
As to class stories, I played the Sith Inquisitor and... I didn't find it that great, on the whole. It starts out very strong, but then degenerates into a series of protracted fetch quests. It is also mired with a few irritating details (why can't I turn Ashara to the dark side, that is Sith 101) From what I've heard the Sith Warrior has a much more interesting story.