Story tends to be an emergent thing from character creation and what type of work the players want to do.

So many potential stories come out of that process - relationships with the other PC's, enemies, rivals, it can be difficult to start with a canned story just due to the way character gen works.

You start by picking a homeworld, and rolling base stats, then pick an initial career (or academy - like college), and then you progress in 'terms' of 4 years. Each term you have a chance for a variety of special events (positive and negative) to occur. Things can take unexpected turns.

A good example was a character I made in the 1st ed. Mongoose traveller - I decided I'd make a naval officer (was gunning for pilot skills) and ended up getting kicked out, being a drifter for a bit, and ultimately taking up piracy. I JUST missed out on a my own damn ship (a Corsair - this would have been a HUGE deal as ships are super expensive) but I got screwed over by the second in command. I ended up with bladed weapon skill at 3 and a gimp leg (pure coincidence but fitting).

That character was a fucking badass, but not at all like I planned initially. When he mustered out of pirating he decided it was time to go legit - and so joined the rest of the PC's to form a team of free traders.

It's kind of different in that instead of having young up and comers (which it is possible to make but they are quite weak characters) you get a group of middle aged has-beens with some real backstory and depth to them.