AniDB has a nice releation graph regarding the different Gundam shows and movies.
Universal Century and related timelines
If you are interested in the original story of the Universal Century (UC) timeline and are willing to invest a lot of time (about 74hrs), you can start off with Mobile Suit Gundam (1979-1980) show and work your way through the sequels following the red line in the graph till the latest Gundam Unicorn OVA.
Mobile Suit Gundam: The Origin is the OVA production following Unicorn and as the name implies it tells the background story of some characters and how events lead to the original series. You probably don't want to start with this if you intend to watch the original series and avoid spoilers.
Gundam F91 and Victory Gundam are also part of UC, but are of a new generation (referred as Late UC) with completely new characters and parties. While F91 features similar spaceship and mobile suit designs as well as similar uniforms, and rather falls in the category of a side story, V seems to be completely unrelated from my point of view, this also applies to Gundam Reconguista in G which is set in Regild Century, a period 500 years after Turn A Gundam.
The summary movies of the original show feature new scenes, but I don't recommend watching them instead of the show, rather watch them when watching side stories.
140 TV show episodes ((43+50+47)*25min)
13 OVA episodes (12*30min+25min)
1 film (120min)
7 OVA episodes (6*60min+90min)
Total: 74hrs 15min
UC unrelated timelines
A page listing most Gundam series timelines and related works is also available in Gundam Wikia. Currently these timelines are in order of production dates: Future Century, After Colony, After War, Cosmic Era, Anno Domini, Advanced Generation and Post Disaster. Shows set in these timelines may share some Gundam specific traits, but they were created to be aired on TV and watched independently to attract new viewers or younger audiences, while loyal fans of the original series are treated with OVAs set in UC.
In the comments above senshin found a guide (see below) that includes most of the shows (at least the various SD Gundam shows are missing, which benefits clarity) up until Gundam AGE and Gundam Unicorn, listing pros & cons for each show.
Spoiler warning: I found spoilers in V (con) and 00 S2 (con), there may be more.
Link: Gundam Series guide from /m/