Watch in this order:
0079 movie trilogy
0080: War in the Pocket
08th MS team
0083 Stardust memory
Zeta Gundam
Char's Counterattack
Victory Gundam
MS Igloo
Shows you can watch at any time because they have no specific timeline:
Turn A Gundam (currently watching this for the first time, fucking amazing. However, even though it's its own entity, it manages to bridge ALL the gundams before it - UC, Wing, whatever - into one cohesive story).
Gundam Wing (still fun to this day. it was my first gundam, not high on the list but worth checking out)
Gundam Seed (don't believe the hate, the show is actually pretty good, particularly in the second half)
Gundam 00 (currently the thing we're all watching now)
Distant can probably give a better post, but whatever. Most of the stuff in the first part of the list are relatively short because they're either 1. movies 2. ova's only Zeta and Victory are the tv series in my list for UC.