How Can I Condense That a Little?

Even taking into account that this is not every Gundam story set between the original Gundam and Hathaway, that’s… a lot of anime. Like, nearly 150 episode’s worth, before you get to a movie to cap it all off, and that’s an intimidating ask of someone just to watch a new movie. If you want to try and condense it, shortly after it first aired just over 40 years ago, the original Gundam was re-cut and presented as a compilation trilogy of movies, called Mobile Suit Gundam, Mobile Suit Gundam: Soldiers of Sorrow, and Mobile Suit Gundam: Encounters in Space. While these movies cover the general narrative arc of the original show in a much shorter amount of time—and are a good starting point to dip your toes in and see if you actually like the franchise in the first place—it’s condensed and it changes some things up, cutting some side narratives and plot beats that still make the original series, in spite of its contemporary late ‘70s animation, a very compelling watch today.
Alas, it’s the only one of the original three Gundam shows with a relatively easily accessible compilation. Zeta Gundam did receive a movie trilogy adaptation for the show’s 20th anniversary called Mobile Suit Zeta Gundam: A New Translation, but they’re currently only officially available physically (and also significantly re-work parts of Zeta’s narrative). ZZ Gundam, meanwhile, never received a compilation, so you’re stuck with the original show. If you’re short on time, the original Gundam compilation trilogy and Char’s Counterattack will provide you the bulk of a newcomer’s context for Hathaway, but be advised: you’ll still be missing out on a lot of character work and worldbuilding that way.