Wow. Let's see...

Trooper and Smuggler: Act 1 by miles and miles. Very tight personal story with NPCs that are very likely to grab you one way or the other.
Jedi Knight: I'm really torn between 1 and 3. Act 1 had some of my favorite villains in the whole game. Act 3 was, well, teh epicz.
Sith Inquisitor: Act 2. That particular hunt was a lot of fun.
Imperial Agent: Act 2. As others have said...gripping, deeply personal, and without some of the "whoa what"-scale stuff of Act 3.
Sith Warrior: Hmm. I found Act 1 had the more satisfyingly concrete goals with credible sources, but Act 3 started kicking a lot of ***. Due to That Infuriating Absence of Choice in Act 3 I'm gonna have to go with Act 1.