Michael has already shed some light on the various incarnations of the Traveller rules. The sheer number of different versions can be somewhat overwhelming.
But once you settled for a given ruleset you face an even more daunting task: making yourself and your players familiar with the vast setting of Traveller.
To my experience this is one possible point of failure when the scope of the setting encounters the expecations of the players for the first time.
The official Traveller universe
The official “Third Imperium” setting for Traveller encompasses 11000 star systems, at least six major polities and a plethora of human and alien cultures. Most of those features are deeply rooted in classical science fiction literature of the 60ies to 80ies – but where this might be very rewarding to me – a SciFi nut for more than forty years – there is little to nothing to relate to for a younger prospective player.
Neither Star Wars features strongly in the original Traveller setting nor does Star Trek and those are probably the most popular SciFi franchises around. And who even remembers Firefly or Battlestar Galactica any more? Coming from the “mainstream of pop culture” the sheer bulk of background “stuff” of the Original Traveller Universe (OTU) without easily recognizable features like a mystical knightly order or a benevolent planetary federation often leads to dismissive reactions (tl;dr).
So how to make this game your own?
There is – as always – more than one answer to this question.
Michael asked me to take a look into a couple of Third Party Settings but there are also a couple of DIY approaches like “Proto-Traveller” (Michael already mentioned it before) to adapt Traveller for your own science fiction gaming needs.
The Traveller rules where originally meant to be generic RPG rules for contemporary or futuristic settings and Mongoose themselves willingly provided a handful.
One of the more successful attempts was 2300 AD (meaning it is still around in 2016) which is probably sufficiently known. But since 2300 AD is Mongoose’s in-house Alternate Traveller Universe (ATU) setting these days I won’t cover it here.
As mentioned above there are also a couple of DIY methods but those were not part of Michael’s request und would be beyond the scope of this post.
Then there are those by third party publishers (3PP) like Spica Publishing (Outer Veil), Terra/Sol Games (Twilight Sector), Zozer Games (Orbital 2100) and Gypsy Knights Games (Clement Sector).
This list is neither representative nor complete those are merely the settings that caught my eye one way or another while I was looking for something new since the Spinward Marches and the Solomani Rim as well as the classic era had somehow lost their appeal.
Except for Twilight Sector they all have in common that they are well below the techological level of the “Third Imperium” setting, that there are no (playable) aliens and that Earth and its neighbourhood feature more prominently.