A lot of the stuff in the Universal Century (UC) timeline of Gundam will make a lot more sense if you've seen the first three shows and movie:

Mobile Suit Gundam (some people will recommend the compilation movies - the show is much better imo)

Mobile Suit Zeta Gundam

Mobile Suit Gundam ZZ (some people recommend skipping this one - they're wrong)

Mobile Suit Gundam: Char's Counterattack

The Hathaway movies serve as a direct sequel to Char's Counterattack (they're based on a novel written by the series original creator), and CCA builds on events in the three TV anime preceding it. I know it's hard to recommend ~150 episodes of a cartoon and a different movie, but you'll probably enjoy the Hathaway movie more.

If you do the homework or not, it's a pretty cool movie with some good visual set pieces. Enjoy!