Mobile Suit Gundam

Yeah you've already got a good order. Those are basically all of the main UC Timeline Gundam works, in order of release, and they do get continuity of characters and themes.
There are also side-stories that you can watch at any point now that you already know of the One Year War, such as 08th MS Team, 0080:War In The Pocket and 0083 Stardust Memories. In general, I'd go to the Gundam wiki and just follow their listing there.

Also a lot of people recommend watching Unicorn Gundam after Char's Counterattack, but it isn't necessary for Hathaway's Flash.

Looks like a good start! Honestly, my biggest suggestion for people getting into Gundam is just to watch whatever UC content seems interesting to you and let curiosity take you from there.

I think my only “hot take” might be that in my opinion, people should watch a good chunk of UC before moving to AU content. My reasoning is that you’ll get a lot more out of AU content when it’s viewed through the metatextual context of UC.

The best order is: MSG three part movie (instead of the episodes), Zeta, ZZ, Chars counter attack

Then you can watch anything. I watched unicorn then Hathaway, then Narrative. For the UC timeline, a lot of people advise the timeline which is linked below. I currently finished 00 (amazing) and caught up with WFM and plan on jumping back into UC and go through the below order.

https://www.mahq.net/gundammain/

I really enjoyed 8th MS Team, the animation is just masterful (disclaimer: I’m a sucker for old school, high quality animation)

Might as well throw in Stardust Memory. It's of mixed quality but does a lot to bridge Gundam and Zeta.