You're not going to find a better place to start, and may not find a better show among the whole franchise, than the original Mobile Suit Gundam.
But there are alllllll these AUs over the last 25 or so years! Each one picks and chooses thematic and aesthetic elements from the early stuff and puts it in the context of its own time. Witch from Mercury just ended and is very contemporary, and very good! You might dig that!
But if you have a soft spot for Outlaw Star, there's Gundam X. If your favorite era is the mid-00s when digipaint started looking good, check out Gundam 00. The AUs generally deliver on being of their moment, so if you have a favorite moment there you go.
Mobile Suit Gundam Hathaway came out recently and is just beautiful. It's a film, not a series, and has little to no barrier to entry despite technically being a direct sequel to a movie as old as I am. It just puts you in a situation and trusts the viewer to feel their way through it. One warning I'd give is it's the first of a planned trilogy so a lot is left unresolved at the ending, but Fast X and Across the Spider-Verse were even worse about that so I guess nobody cares anymore.
Now let's talk about the most common answers to this question that I think are wrong. The original show has a trilogy of compilation movies, which are indeed a quicker watch than a 43-episode series. So what. It's a great show in its own right and deserves to be experienced that way, not treated like homework or a hurdle. Imagine if there were a show that only used keyframes, no in-betweens, and how much life would be lost. That's how the emotional beats and character arcs work in the movies, cut from extreme to extreme and I think it does a disservice to suggest it as a new fan's first exposure.
0080: War in the Pocket has a lot going for it. It's bite-sized, great effects animation, a beloved OVA. But the suggestion that it's an ideal place to start rankles me. War in the Pocket goes hard on one segment of Gundam's thematics, and it's some of the least uniquely Gundam stuff. I wouldn't feel right treating any work lacking Newtypism or some equivalent as a gateway to all Gundam. I can't do it.
Also, a couple years ago I wrote an article that ended with answering basically this same question from another angle.