Back to the OP on this one.
I am limiting my suggestions to a few titles that have Traveller applications. While there's a lot of books that ought to be read for someone's 'sci-fi literacy', there are quite a few that are kind of out there insofar as RPG utility is concerned. I'm also limiting my lists to 4 or 5 selections so as not to overwhelm anyone.
In no particular order:
BOOKS:
- Starship Troopers, Heinlein
- Downbelow Station, Cherryh
- Dream Park, Niven
- The Stainless Steel Rat, Harrison
- I, Robot, Asimov
- Hammer's Slammers, Drake
TV:
- Star Trek Original Series
- Firefly
- The Expanse
- Battlestar Galactica [both]
- Almost Human
Films:
- Star Trek [first movie]
- Star Wars [ditto]
- Interstellar
- AlieNation
- Enemy Mine