Why does Classic Traveller have to be adventure in the far future? Most of the weapons in the LBB set are items you can find in any National Guard Armory (except the laser weapons.)
The Icy Shores
Humanity has achieved a maximum tech level of 10. Gravity control was developed in the mid 21st century. This led to gravity confined fusion and eventually jump drives. The first wave of sleeper ships set out for the nearer stars in the 2070's. They had reached their destinations and reported back by 2100 in many cases and a second waves of colony ships set out in the first decades of the 22nd century.
Some of the ships headed for Alpha Centauri and Barnard's Star didn't make it. radiation, drive failure, insanity inflicted losses. Many ships stopped at rogue planets or asteroids .3 to .5 parsecs from Sol. Some ships set out to reach these very planetoids and brown dwarfs and build their own colonies on the Fringe of human society.
In the middle of the 22nd century the jump drive was developed by a researcher on Titan Station. The jump drive was a game changer. The drive was soon sold to Earth and Earth moved out into the Oort Cloud and to the fringes. The drive had a maximum range of one parsec and there were no stars that close. The Fringe Worlds were a convenient stop on the way to the closer stars and Earth wanted to control them for security and economic reasons.
Earth likewise tried to consolidate the colonies into an Earth dominated federation. The colonists were outright hostile to the idea and in some places riots or rebellion began. Pirates and mercenaries of every stripe congregated in the Fringe Worlds to run guns t colonial rebels or find mercenary work with either side. Some Earth factions were for isolation or at least letting the colonies remain independent. The Fringe Worlds just tried desperately to maintain their neutrality and independence in a deteriorating situation.
The weapons and a lot of the equipment in this setting are going to be familiar to players. Earth is reaching TL 10 in some areas. The Fringe Worlds are TL 9. Some colonies are TL 9 at their major settlements and TL 8 or lower elsewhere.