Which one? Each class has its own class story, so there are eight stories taking place across the different planets, with shared side quests.
The only one I got into in any depth during the two weekends that I tested was the Bounty Hunter class story. It starts off simple enough with your character vying for entry into the Great Hunt, which is basically a competition for glory originally organized by the Mandalorian clans. Naturally events become more personal, and you can start treating the Hunt as either purely for your personal glory or as a means by which to gain revenge for an act perpetrated fairly early in your story.
Most of the side quests that I undertook were well-done in story terms, offering the BioWare hallmark of different choices and outcomes that you'd expect.