I had some trouble getting into Traveller with my players about 10 years ago. I had the same idea of having a crew trying to work off their ship mortgage. It seems like a natural backstory and reasoning for being a trader/adventurer in a sci-fi game. However, my players got bogged down in ledgers and accounting and it got stale pretty quick. They would avoid plot hooks I dangled in front of them as "too dangerous" and would rather find the most lucrative trade good between nearby systems.
There are a few ways around this. One of the best is the Pirates of Drinax sandbox campaign. This product heavily details the Trojan Reach sector of the setting. Basically, a backwater section of space that was once a former sprawling empire. Now, its a loose connection of independent systems sandwiched between two quarreling empires. The players are tasked with attempting to unite the reach and restore the empire. It's up the players to achieve that enormous goal through any number of deeds. If anything, you can chop up Pirates of Drinax for your own purposes. The material is a good deal for the money (digital cheap, physical solid material).
One other aspect was the spacehip travel. Players often think of Star Trek and Star Wars where it takes a few hours to travel across the galaxy. Traveller by default is much more akin to the sailing world of the past centuries. It takes a week to get to another system. Once in a system, it may take hours or even days to reach a planet/station. Space is BIG and Traveller treats it as such. Framing travel more in a sense of sailing helps a lot.
Yes, but as I said the players do not have as much influence on character creation as in other RPGs. They might decide that they want to be a trader or soldier, but the dice might say no to that.
Lots of folks get caught in a trap assuming that Traveller chargen makes all the important decisions for a player. I believe a lot of that comes from D&D's class system. Traveller is heavily dependent on skills, not class. The best way to frame chargen to players is around the skills they want to get the character they envision.
For example, a player wants to create a ship pilot type character. Naturally, the Navy seems like the best career to do this. However, you can also get piloting as a merchant marine, scout, pirate, etc. Its more important to focus on the skill packages of the careers, than the idea of a career being a class. Being a navy pilot, gone merchant marine, gone pirate doesnt make you multi-class in the traditional D&D sense. For example, being a merchant marine instead of a navy pilot in Traveller doesnt mean you are a bard instead of a cleric. These are important distinctions to raise during session zero when it comes to playing Traveller, IMHO.
What the dice driven chargen does is create unique backstories for each character. It helps build NPC allies and enemies for the GM to use. It also can help explain how the PCs know one another. This complicates things for players who like to envision exactly every detail of their characters past, but once again this is something of a departure from D&D.
Cheers!