CZ doesn't really have much in the way of Story. An intro dialogue and a debriefing after the Titans of Industry mission (which is just doing the 2 flashpoints, labs and meltdown one after the other).
Have you done Makeb? It was mildly interesting the first time, but subsequent toons was just boring because it's the same story for all classes, only the factions are different. Several of my imperial toons have only done "enough" (the first little bit) to unlock the taxi to the mesa with Toborros Courtyard (on Republic side it's immediately accessible).
Edit: Come to think of it, I haven't actually bothered finishing it yet on any Republic toons. The high mob density and immediate grind just turned me off at the time of release.
I think I got through most of Makeb. Overall it's kinda boring, and right now I'm more interested in trying out an Operation, but the guild I joined doesn't have em going on when I'm online.