Putting this in spam because I want a quick answer and not a whole effin anime discussion.
Okay so, I've been wanting to watch Gundam forever. There is just one little problem..
Of the series in you have in your screenie, most of them are separate series set in different universes without relation to one another. With that:
-Mobile Fighter G Gundam (it's a standalone main series, but weird and doesn't capture the classic themes of 'Gundam'. It's like Gundam Street Fighter with a plot)
-Mobile Police Patlabor (this isn't a "main", or popular Gundam series, watch only after you've watched a few others and still like Gundam)
-Mobile Suit Gundam 00 > Second Season > Movie
-Mobile Suit Gundam AGE (most recent series, ended last year)
-Mobile Suit Gundam SEED > Destiny > Final Plus (FP isn't a series, but an expanded re-work of the final episode)
-Mobile Suit Gundam Unicorn - Compacted into 6-7 ~1hr OVA episodes, not yet ended /// belongs chronologically to the longest and premiere Gundam-universe series (UC), of which other series are not in your screenie. But it's okay, because you can get the major points in this OVA series without watching prior (or from watching other series first)
-Mobile Suit Gundam Wing > Endless Waltz (it's listed twice in your screenie, I assume one is a single movie and the other are the chopped OVA episodes. You can watch either, they're the same)
If you've watched none of them, I think good main series to start at are Wing, SEED, or 00 (they are the most traditional, in respect to the franchise themes).
Wing and 00 have similar story elements and overall themes, though Wing was made in 1995 and 00 in 2007.
...and most series lag at the start, the big, continuing story doesn't usually pick up until midpoint. So if you're bored, just wait it out for a bit,
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