Tekken 6

Just finish the short 2-episode tutorial with lars (and with Alisa) and then you can choose whoever you want

You can view character's story using scenario campaigns arena....

The story is about Lars and Alisa. But once you've opened up the other characters for selection, you can choose them to complete stages throughout the campaign. For those who might have some trouble, certain characters might be a bit more useful than others.

I ran through with Devil Jin. Even though the cut scenes would show Lars, his boss battles had unique dialog that was specifically for Devil Jin.

Scenario Campaign follows the story of Alisa and Lars but once you finish the first level of it, Arena gets unlocked, which is where you can find out the stories of all the other characters once you've unlocked them. Hope this helped.

How do you unlock character movies

While the story line is centred around Lars and Alisa, each character does have unique dialogue on each stage. For example while playing Xiaoyu against Heihachi he will say that Jin is no longer the person she once knew.

The actual campaign follows (in terms of protagonists) just Lars and Alisa. Despite picking other characters during the actual Campaign mode, you should notice that the cinematics always reverts back to Lars, as if the player was using him to complete the stage. So no, picking characters other than Lars and Alisa, won't affect the Scenario Campaign storyline at all. The only thing it affects is dialogue, but only on certain stages and even then, you have to pick key characters (as in like Devil Jin, Heihachi, etc).
And no, the other characters do not have a story beyond the individual endings (after completing Scenario Campaign, that's it. That's all the story for Tekken 6.)