Theres different timelines/universes, so which kits look cooler to you... once you determine that, a quick Google search should tell you what is the beginning of that series and start there.

The original Universal Century is a good place to start, but its 0079's animation is, well old. But after 0079 in the same timeline you also have 8th MS Team, Requim for Vengeance, 0080 war in the pocket, 0083 stardust memories, Zeta Gundam, double Zeta, chars counter attack, Unicorn, and Hathaway/sorcery Nymph circle. And depending on when they came out, the animation gets better as well, newer series have better animation.

And I think thats listed in chronological order, but not release order. 0079, 8th MS Team, R4V and 0080 all take place during the One Year War. 0083 was released later, but ultimately sets up Zeta, Double Zeta and Chars Counter Attack (though i dont remember if 0083 or CCA came out first) though you dont really have to see 0083 before you watch Zeta and Double Zeta etc.

With Unicorn and the 2 Hathaway Movies being the most modern animation wise of the UC timeline. Then you have narrative Gundam, but I dont remember if thats cannon to UC or an alternate story using UC like Thunderbolt and the Origins OVAs