So it seems that various forms of Gundam have been around since 1978. How important is it to watch the old ones, or is each series more or less standalone?
off the top of my head. the first Gundam Series, Zeta Gundam and Char's Counterattack are probably the best ones in the UC continuity. These ones follow their own particular continuity and while not exactly essential do help make it easier for the viewer to understand the bigger picture.
The UC continuity is for Universal Century and the majority of the early Gundam (MS Gundam, Zeta Gundam, Double Zeta Gundam, Char's Counterattack, Gundam F-91, Victory Gundam) shows are based around that setup. some more recent ones have followed in the UC timeline (The 08th MS Team, Gundam: Stardust Memory and Gundam: War in the Pocket).
Other shows have all been set in their own isolated continuity. For example, Gundam SEED and Gundam SEED Destiny are their own continuity. Gundam 00 Seasons 1 & 2 are in their own continuity, Gundam Wing, G Gundam, Gundam: After War, Turn A Gundam or Gundam X each have their own seperate continuity.
The best ones tend to be (in my own personal opinion) the Original MS Series, Zeta Gundam, Gundam Wing, Gundam SEED and Gundam 00.
http://en.wikipedia.org/wiki/Universal_Century has the list of shows that are based within the UC continuity.
while
http://en.wikipedia.org/wiki/Mobile_Suit_Gundam will be able to cover the rest.
To the newcomer it can seem incredibly daunting and large. But each person has their own favorite Gundam shows.