As to the scenario, here are my thoughts:
I will be using Classic Traveller 1981 Books 1-3 (with some text taken from 1977), though I am seriously considering the range band space combat from Starter Traveller.
I have been taking a lot of Christopher Kubasik's ideas (over here:
https://talestoastound.wordpress.com/traveller-out-of-the-box/ also worked out on this forum under the id creativehum) to mind (and the other folks who have also been posting in the same vein), so reading his blog will be useful for getting a feel for where I cam coming from.
I have in progress, reasonably happy with, modified skill tables for Supplement 4 which I am open to discussion with players about.
Setting will be my own, currently working on a 2 subsector area somewhat inspired by the Seven Sisters and District-268 subsectors of the Spinward Marches that is at the frontier and beyond of "the imperium" (whatever that is...). The encounter tables and procedures in the books (and more tables I pull from other places or just flat out make up) provide a lot of implicit setting. I've posted a map here in this board.
My concept within the setting is that the PCs are mostly ex-military (with Merchants and Other thrown in of course, plus possibly the odd Supplement 4 career or two) all having mustered out on the same world, or having made their way there. I will leave it up to the players to add more definition as to why they know each other, but I think that should be a given (or if someone is unknown the the group, the players have primed things so we don't play the "we all meet in the bar and get into a fight). I'm assuming someone will muster out with a ship and the group has an interest in exploring the sandbox and figuring out what they can make of it (trade, trying to find a world to exploit, just wandering, whatever).
But it's a sandbox, and it's your game as much as mine, so ultimately we will work together and I hope something exciting will emerge from play.
Frank