I've played every class to Act 1 or beyond except the IA, SI, and Trooper. Of those stories, the Sith Warrior was the most epic (finished Act 1 in beta), followed closely by the Jedi Knight (finished the entire storyline). The Bounty Hunter had a good Act 1, slow Act 2, and good ending for Act 3, but otherwise it was just above average. Smuggler Act 1 had a good pay off but it was still very slow and despite wanting to make this class my Pub main I haven't been enticed to go start its Act 2 storyline yet.
If you really want to have fun with the SW story, though, I suggest you go Light Side. I can't give spoilers out of principle but also because you don't want to hear them, but trust me that you will be pooping bricks because you chose to be a Light Sided as opposed to Dark Sided Sith Warrior; it is THAT good.
Without spoiling it, since someone did mention how the JK is your "KotOR 1" story all over again (it is basically the same exact story even written by the same exact person, thanks for the epic stories Drew!), I can say that the SW story is sort of like the evil version of the same thing. However, it's more than that; there's a lot of soul searching to see where you fit in and the need to prove yourself to the galaxy whereas with the JK it's an understood that you are "Master Jedi," the wise sage who can do no wrong.
With the JK, the missions between planets and Acts focus on stopping Dark-Sided individuals, period. With the SW, interplanetary missions focus on your own morality, what you are bringing to this universe, and so the LS and DS decisions differ much more greatly and have a more profound effect on your entire storyline.
Thank you very much. I carefully choose, or try, what I say. I'm not mindless like some people that go straight dark or light. I will definitely try out a Warrior.