Ultimately, it's going to depend on the type of campaign you're planning on, and how in-depth you want to go. At a minimum, I'd probably consider the "green books" - i.e., the rule books, like
High Guard,
Mercenary,
Scout,
Scoundrel, et cetera - as 'must-haves', so that you have the flexibility of character type for your campaign. Beyond that, you'd have to look at your needs, and make decisions - if you want to campaign in the official Traveller setting, I'd get
The Third Imperium: The Spinward Marches. If you'd prefer to do a 'hard' Merc campaign,
Hammer's Slammers might be a better choice. Want a touchpoint of familiarity for your players? It's a good bet that Babylon 5 won't be unfamiliar to them, so your book of choice would be
The Universe of Babylon 5. Pure homebrew? None of the extant setting books is ideal, but any or all of them could provide inspiration for your own development - and so could plenty of commercial SF, as well. And some (lots of) high-quality examples of the latter are easily available,
free, courtesy of
Baen Booksand a gentleman named
Joe Buckley.
tl;dr summary: It's ultimately up to you, and depends on your needs. Without knowing more about your needs, nobody can make a
sensible recommendation.