The only thing you HAVE to watch before Zeta is the original MSG, or atleast the 3 movie version.

As for the UC timeline masamuneehs said I have to correct some things:

Mobile Suit Gundam - good but slow at times
MSG: The 08th Mobile Suit Team - side story, good
MSG 0080: War in the Pocket - side story, more of a drama but still good
MSG 0083: Stardust Memory - semi-side story, decent
Mobile Suit Zeta Gundam - dark and fantastic
Mobile Suit Gundam ZZ - first part hard to watch(unless you like stupid stupid humor), but once tomino takes over it becomes very entertaining
Mobile Suit Gundam: Char's Counterattack - concludes the original MSG saga, very good
Mobile Suit Gundam F91 - Originally planned as a series but was then turned into a movie(not that good)
Mobile Suit Victory Gundam - THIS is the last UC series, just as dark as Z, and is my 2nd favourite UC series

EDIT: Voted for Zeta(of course) but SEED is definately a close 2nd.