Mobile Suit Zeta Gundam is the best of early/older Gundam and set the definitive "tone" of the franchise, so I'd recommend that one first, but to understand what happens in it, it's best to watch Mobile Suit Gundam 0079 first. I would say watch the movies of 0079 instead of the series (or honestly, read a summation somewhere--I'm serious), as that series is very much a product of its time, and suffers from really bad animation (it WAS the very first so I get that it was animated on a budget). The plot also drags A LOT in some places. I personally love 0079 but can acknowledge that it's a bit of a slog and has some outdated tropes.

Edit: If you want something slightly more modern, Gundam Wing is pretty good and you can go into it without any backstory at all, as it's a standalone series. There's a reason beyond the bishonen main characters that it was so popular when it came to the US.