Knight is the best republic story IMHO. It's basically KOTOR 3 and has quite a bit of variety of choices and companions ranging from an astromech droid to a sith. It's also the story that makes the most sense for KOTFE and KOTET. The only problem really is that the story has quite a few cliches.
Smuggler is next. You can basically be anyone you want...A loyal republic privateer or a bloodthirsty pirate. The story is worth it just for the snarky remarks the smuggler is constantly making. However, in terms of the actual story, it's pretty irrelevant, since you don't do anything too important.
The Trooper story starts with an interesting plot, but after chapter I, it loses its originality and becomes pretty normal. But if you like war stories it's decent enough. The simple fact that Jennifer Hale is the voice of the female trooper should make you want to play it, though.
Unfortunately, the consular is the last one for me. It's a good story, but when you compare it to the others, it just can't hold its own against them. I mean the premise of the story is pretty good, a loyal Jedi who is strong with the force and saves the republic by saving the Jedi from a plague, uniting the core worlds and defeating the emperor's children. That sounds amazing, right? Well, it is, but when you are playing it doesn't really feel amazing. The boring voices from both consulars and the bland companions certainly don't help it either.