>>5402
0083 is good for a shorter, action packed series. It also sets the stage for Zeta Gundam and acts as a prequel to it. It's like top gun with mechs. 08th MS Team was good as well, but it seemed lackluster to me due to the main character having such resilient plot armor.
I couldn't make it through all 43 episodes of 0079 (too much QUALITY animation), I ended up watching the compilation movies. It leaves stuff out but you get a pretty good idea of the one year war period.
Zeta is the best series but it refrences a lot of the original series. If I didn't watch the movie trilogy there's a lot of characters who appear in zeta who I wouldn't give a shit about (The white base crewmembers, Char) if I didn't watch the first series. Avoid the movie compilation of zeta, it changes the ending and retcons the third UC series, ZZ. Zeta is the best gundam series, high body count, great moments and takes on a dark tone during the ending arcs.
ZZ is viewed by a lot of people as optional, it starts off as lighthearted and cheery and then amps up into dark and brutal plot points. Only UC series that shows the entire process of a colony drop, from the start all the way through the aftermath. It's also the first gundam to be based around a team format, with multiple people fielding gundams.
TL;DR
If you want something quick watch 0083 or 08th MS Team. 0083 is the better of the two IMO.
If you want to see what made me personally love the series, watch the first trilogy then Zeta.