For Gundam:
Mobile Suit Gundam Movie Trilogy(Classic Gundam streamlined down to the essentials. Yeah you miss some stuff, but the animation is cleaned up and the essence of the series is kept with less filler and bullshit gunpla whoring. This is probably the best way to experience MSG)
Zeta Gundam
ZZ Gundam(Zeta is considered the darkest Gundam and is a fine work of storytelling. ZZ is much less serious but an important work in its own right with some compelling characters)
08th MS Team(Though it does not fit into the UC Gundam timeline, this is an awesome show nonetheless and you might want to start with it because it's short and accessible)
War in the Pocket(A poignant and moving OVA that holds true to the anti-war spirit of Gundam)
Victory Gundam(The second darkest Gundam. Though disjointed, it is pretty good)
Turn A Gundam
G Gundam(These are a little less serious. Turn A Gundam is more like an adventure type show like Eureka 7 or something, G Gundam is a hotblooded super robot show)
Gundam 00 SEASON 1(Awesome series that simultaneously deconstructs and reconstructs Gundam. Season 2 takes a big shit on it but sets upt he movie, which is quite good)
Also my personal non Gundam recommendation: Giant Robo: The Day the Earth Stood Still OVA