well i would say start with one of the more recent ones, they are just easier to watch, unless your really into retro anime, then go straight to the original series.
So:
Gundam Wing: Very good plot, excellent pacing and characters, and some pretty cool action. The story is more plot driven then character driven though, this is not a bad thing, just a matter of taste. The compulsory love subplot feels very...well compulsory, it doesn't add anything to the story and just feels tacked on, however it does get very little screen time so its all good.
Gundam SeeD: There is a reason this is probably one of the most poplar gundam series out there, but generally regarded by gundam fans as one of the worst, although not bad by any standards. It's essentially just gundam watered down, and given a teen drama spin. As far as the teen drama goes, its very well written and handled intelligently, however if you are older than 18 then all the emo melodrama will most likely get on your nerves a bit. The sequel series, SeeD Destiny, is barely worth watching unless you really enjoyed SeeD.
Gundam 00: The most recent series. It is fairly unique from other gundam series in that it is set in our future, and based on our current world affairs and problems. I feel the creators definitely wanted to take a more serious and realistic approach to the series. The plot is based heavily in politics and world affairs, and any sort of character development get pushed almost entirely to the side. However it seams to me that the creators lost confidence and decided to tack on some generic, pointless, anime-esque villains and plot devices just to play it safe, it detracts from the series in my opinion.
All in all these are all very good series to start off with, you dont need to know anything about gundam to understand them and they are all very enjoyable.
