Mongoose Traveller is surprisingly good. It's by Gareth Hanrahan, who has freelanced on many projects (The Laundry RPG, for example). Thus, it's well-written and clear. Gareth is good at flavour text, so it's atmospheric, too.
It sticks close to previous editions, while fixing some niggles: for example, it doesn't let characters die during character creation.
Thus, it's not revolutionary, but it's clear and builds on the strengths of earlier versions. For what you want, it's a good option.
Character development in Traveller has never really existed. You play, and the playing is the thing to enjoy whether it's a one-shot or a long-term campaign. You might develop contacts and resources, but you equally might not – character development simply isn't the point of playing. Your character is your means of exploring (or exploiting) the universe. Whether by the end there has been any development is merely a matter of personal opinion of the observer – the game takes no position on it and provides no rules for it.
Improvement of your character's lot is something you can aim for, but it's not built into the game at all. It's only one thing you can do, just like in real life some people can have ambitions to improve themselves and their lot in life, and some people might just want to explore, or to hold onto what they have. Improvement is built into a lot of games as the objective every rule revolves around, but it's not so in Traveller. Traveller is a sim game in the very original sense, where the game makes no assumptions about what your character aims to do, and does not build any such goal-assumptions into the rules.
Change can be upward, or it can be sideways (or downwards!), just like in real life. There is no built-in rules for development in any direction – it's merely a matter of the stuff that happens during play in the fiction, which you can post facto interpret as development if that's what you want to do. A ship captain might merely have the motive to keep flying, and at the end of a campaign they may have had many adventures, accomplished many things, and they may have deeper or changed views on life, but they're still just as poor as they used to be and still flying the same, trusty ship they always have. You can get better stuff and connections, but an upward trajectory is not the aim of the game and not embedded in its design, and assuming it is will just be confusing. The tradition of improvement isn't built into Traveller.
A character that is numerically static is alien to the sensibilities of gamers brought up on most current RPGs, but some games simply don't have the character-advancement subgame and that's not a flaw. An assumption that development must be somewhere built into the game will lead you astray looking for it, so try to let it go and understand the game on its own terms. Character development is outside the rules, in the minds of the people who play the game.
Best Answer
Far Future released this short PDF called The Galaxiad that provides sketchy information on names mentioned in the Traveller Galaxy. Marc Miller explains more in this Kickstarter Post.