More helpful hints from a old Traveller grog:
1. Don't worry whether or not you are always on-point with the lore of the game. The Official Traveller Universe is literally as old as Greyhawk and there's a lot of stuff in there. Don't worry if you see us old grogs arguing about this point or that. It's what we do but at the end of the day these are just our opinions. There is a phrase we use a lot on the board here, 'IYTU' and 'IMTU'. It means 'In Your /My Traveller Universe'. How you play Traveller [or any other game] is gonna be different than the way I do it. That's. Just. Fine. If it's fun for your players, do it. If you want the Imperial Marines to look like Killer Clowns from Outer Space [with Fusion Rifles], have at it and enjoy.
2. Once you gather your players, take a moment to read your audience. Some players are gun nuts and want to blast their way through the universe, others want a 'heist movie' a'la Ocean's Eleven. The Q and A for this will take up much of Session Zero.
3. I'd suggest setting up a sandbox. Pick a subsector... any subsector where the majority of planets are J-1 or J-2 from each other is good.
4. If you want to use the OTU for your Traveller game, I suggest buying one of the regional books [Behind the Claw, Trailing Frontier, etc.] and setting up your sandbox there.
5. Don't be afraid to ask questions on the board here. We're happy to help.
Welcome aboard the Beowulf.