A lot of Gundam you can watch out of order. My personal favorite is 0083.
Gundam 00 is one of the best of the recent Gundams.
MS Igloo is another one of the better recent series.
08th MS Squadron is one of the best in the series even if it’s more about tanks than mobile suits.
Char’s Counterattack is a good movie, but may leaves you kind of confused if you don’t know the back story between Char and Amuro.
A lot of people swear by 0080: War in the pocket. I thought it was just ok.
Gundam Wing is watchable if you can survive past the first quarter to half of the series.
F91 was just ok.
Gundam Seed should be avoided. However, Gundam Seed Stargazer is a stand alone OAV and I liked it.
G-Saviour (2000 film) was an English made live action movie that should be avoided like a horrible plague.
Technically the order is the original series which is compiled into 3 movies (I fell asleep watching them), Zeta Gundam (more movies), Gundam ZZ (double Zeta), Char’s Counterattack, 0080: War in the Pocket (you can watch this after the original 3 movies), Gundam F91, Victory Gundam, Gundam 0083: Stardust Memory, 08th MS Team, Mobile Fighter G Gundam, MS Igloo, then After War Gundam X. I mixed chronological and production order a bit there.
Then, there are Gundam series outside the main Gundam Universe that can be watched in any order:
Gundam Wing, Turn A Gundam (great music by Yoko Kanno), Mobile Suit Gundam 00, Super Deformed Gundam, and Gundam SEED.
I think I listed all of the anime, but there’s manga too. d:
Edit: Dang it, Sean. Why’d you have to go and negate all of my work? lol.