if your asking "what are the minimum number of books needed to play this game?" then the answer is that everything needed to play is included in the Core Rulebook. everything after that is effectively a add on that expands on some part of the core rules, for example starships, equipment, etc.
Also, a lot of the material is cross edition compatible, or convertible with only minimum work. Classic traveller adventures, by and large, would work with MgT, as long as the ref reads though before hand and swaps a few skills to the relevant new ones, ect. the biggest area of incompatibility is ship design, IMO, but since the core book has a collection of common ships already in it, it shouldn't be that hard to just use those.
almost everything background related is effectively unchanged, and world profiles (and by extension, the sector data) are the same, so its really easy to use the older stuff for that.
my advise would be pick up the core rulebook, and then maybe the classic traveller CD, because as you point out, its got a LOT of content, much of it useable in MgT as well. then, after playing a game or two, see what parts of the game intrest you and your fellow players.
High Guard focuses on spacecraft and includes the ship design process, as well as rules for capital ships (ie USS Enterprise sized ships, compared to the players Millennium Falcon).
Central Supply Catalogue is full of intresting guns, armour and gear, and good if your often getting into firefights. a lot of the weapons are not so much different as "flavoursome", in the sense they can add a bit of flavour to a character or bad guys with a distinctive weapon.
of the other major books, Im not sure what to recommend, apart form some older edition stuff. the 1e sector books (spinward Marchs, Solomani rim, Deneb, etc) are all about 15-20 dollar on DrivethruRPG, and 100% compatible with 2e, and most of the published adventures would require no more than a hour or two extra prep to make work. Sme of the Alien module books come with a full sectors data inside them as well, on top of all the stuff about the alien race, so they might be a shout as well
