Christ, every time with this shit. It's pretty simple really: Production order. Always.
0079. Series, not the movies, though the third movie is actually quite good. There's a lot to appreciate about the kind of bumbling series that 0079 is, but if you're not into older anime it might be a bit of a slog. It's kinda goofy, kinda poorly animated, but the core of the show resonates incredibly strongly, or we wouldn't still be talking about it today.
From there, Zeta. DEFINITELY not the movies because they're from the mid-2000s, have awful subs, and are not very good in general, but the show itself is quite good. My favorite, actually, especially in terms of Universal Century (the main continuity). Better animation, higher budget, killer tunes, 80's as hell. What's not to like?
Past that, you're more or less free to continue through the years watching sort of... whatever. Do you want more OYW/0079 style stuff? The OVAs. 0080, 08th, 0083. With the context of 0079 and Zeta you get a lot out of those. Do you want to continue the plotline of Amuro/Char/UC in general? ZZ, Char's Counterattack. ZZ is divisive, but if you can tolerate some stupidity, it's still a fun series, if not on the same caliber as its predecessors. And CCA is a beautiful movie, bit of a weird plot, but a very definitive "endpoint" for UC, at least for the time.
After that, you're in the 90's. This is when sunrise started to branch out from simply the UC chronology and made gundam shows that weren't necessarily in line with the previous canon. You have Victory, which is UC, but far enough in the future that it's not too terribly related to anything. You have G, Wing, X. Try them out, see if you like them. And then try on Turn A. It's a series that's very different, but you get a lot out of it after having already immersed yourself in the legacy gundam has built up to this point. My second favorite show, stellar designs and music, and such a fucking interesting show.