Well, you could start from the beginning with the original Mobile Suit Gundam. Like someone above said though, it's really really old-school. Alternately, you can start with 08th Ms Team. You need little to no knowledge of the lore behind the universe. Just watch it for the story and relatively down-to-earth-but-still-damn-awesome mecha battles.
If you start with any other Universal Century series, you might be slightly confused if you don't drop by Gundam Wiki and look up some of the terms they talk about. As you start further and further down, you'll also lose backstory.
If you want to watch a single series instead of following an entire universe, then you can probably start with Gundam Wing. Most kids from the 90's watched it as their first Gundam show on Toonami.
Or Gundam 00, which has essentially the same story concept but that particular universe is a bit darker and reacts accordingly (easiest comparison is between their Pure-Pacifist Princesses. One becomes Queen-of-the-World, the other is mostly helpless to the plot). The scale of the mecha battles and general polish is much higher in 00.