AniDB has a nice releation graph regarding the different Gundam shows and movies.
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.
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.
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
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/