I think its a good idea by watching what's considered are great (or the best?) example of a genre, then perhaps the best of great directors and last perhaps movies which are interesting from a (movie) history standpoint.
Examples (sci-fi and action heavy since thats fun):
Star Wars: Sci-Fi, movie history & technology (A New Hope and Empire Strikes Back at least)
Indiana Jones: Adventure, movie history and Spielberg (only Rasiders of the Lost Ark)
Alien: Horror & Sci-Fi, technology (2 years after Star Wars) and Ridley Scott (additionally Aliens if you like it, more action)
Se7en: psycho/horror/thriller, David Fincher
Schindler's List: history, Spielberg
Saving Private Ryan: history, war movie, Spielberg (a modern contrast could be Jarhead and a modern "imitation" Black Hawk Down by Ridley Scott)
Pulp Fiction: movie history, comedy(kinda), Quentin Tarantino in a nutshell
Hot Fuzz: satire, action comedy, Edgar Wright (same goes for Shaun of the Dead with Zombies instead of action)
Heat: movie history, crime drama/action, Michael Mann (features the argubly best shootout in movies so far)
Matrix: sci-fi, action, movie technology & history (interesting anime and philosphic influences - don't bother with the sequels!)
Akira: cyberpunk, anime, movie history (is on youtube?)
Blade Runner: cyberpunk, movie history & technology, Ridley Scott
Rear Window: mystery/thriller, Hitchcock (you could watch many other Hitchcocks instead but its a good example I think)
Lawrence of Arabia: epic(!) historical drama, movie history
12 Angry Men: courtroom drama, chamber piece, movie history (old but very enjoyable)
The Lord of the Rings: fantasy, adventure, movie history (yes you have to watch all three and the extended cut in the case of Return of the King)
Life of Brian: movie history(?!), history(?!), Monty Python(!)
Goodfellas: crime drama, Scorcese (lots of other Scorcese stuff is a very viable alternative)
...and yes, there is still missing a ton - primary older stuff.