Favorite moment is Lady Une throwing a dude out of the back of a cargo plane without a parachute, and then pulling out a handgun and shooting him in the head as he plummets towards the ground, because hey, can't leave anything to chance, right?
I don't really dislike any Gundam show I've watched, except Seed. I plan on rewatching it soon though to see if my opinion of it can change. I love Wing, G Gundam, Zeta Gundam (well, at least the first 40 episodes anyway; when everything went out of print a few years ago the fifth volume on DVD was going for absurd amounts of money, so I've never finished it), and absolutely love 08th MS Team.
I started watching 00 at work last night and like it well-enough; my coworker and I made it to episode 10 and will resume watching tonight.
I just started playing Gundam Breaker 3 (imported an English-language copy of the Break Edition from Malaysia) last Friday too and am having a blast with it. I guess I saw a rumor on the PS4 subreddit last week that there is some Gundam game news coming out soon? I'm really hoping it is a new Dynasty Warriors Gundam (I know deep down it won't be) because I've sank hundreds and hundreds of hours into that series.
Favorite Gundam designs? Epyon at the top of my list, Gundam Rose, the Dom, Rick Dias, Quebley, Gelgoog, and then the Deep Striker from Gundam Sentinel.