I usually do one of two things.
If the PCs don't have a ship, I pull out 76 Patrons and figure something out. If they do have a ship, I have them start by finding cargo and I improvise from there (read my actual play post on the Voyage of the Vulture for an example).
In my opinion, what makes Traveller, especially Classic Traveller played in the Third Imperium, different (and thus distinctive and thus worth playing because it offers something that other games don't) from other games is in how much it is geared towards completely player-driven play.
That's the way the game was written, and it works really well. The players have a goal, and it probably involves making a large sum of money (to buy a ship, to improve on the ship they've got, whatever- characters who aren't interested in this goal are not appropriate characters for this kind of game).
So, let them try to reach their goal. The systems are already in place. The PCs can seek out patrons, cargo, whatever on their own.
The GM's job becomes twofold- one, to ajudicate the rules systems as the PCs try to make megabucks, and (the good one) two, to throw wrenches into the works.
The characters' motivations for getting into an adventure are never artificial, because the PCs got themselves into a situation rather than the GM thrusting the PCs into it.
Everyone loves money, right? But most people also have a basic sense of scruples. So there, the perfect recipe for adventuring onthe Imperial fringe!
The best part is, many of the Adventures and Short Adventures seem to have been written with this style of gameplay in mind.
So, every now and then, if you want, throw in stuff from the Kinunir. Or even better, start dropping hints about Twilight's Peak, and see if the PC's eventually bite.
I lied before. The best part is, other than veing reasonably familiar with the game material, this style of gameplay is easy on the Referee. And because most RPGs these days are NOT set up like this, it is refreshing and different and even appealing to many players.
