My Nord warrior was just at the wrong place and the wrong time. He supported the Stormcloaks and was just trying to get a better look. He got captured and mistaken as one.
All my other characters didn't even go on the carriage. I just rush through the unbound quest and once I am out think of a story.
My Mage for instance wanted to study magic and the college and arrived on a boat with a friend. Her friend camped out in a forest a few days before heading out to go home.
And that is we're my mages story starts. In a forest camp ready to live her life in Skyrim.
My assassin was a poor kajhit hiding out in Windhelm. He Already knew how to hide because he had to hide from the townspeople a lot. He eventually hears of the Antino boy, and that's were his story starts.