08th MS team is short, (12 or 13 episodes) and set in the UC timeline (the same timeline that the original series is set in.) It is a pretty good look, IMO, of what Gundam is all about (though perhaps a bit more sad than the other series.) It works as a stand-alone series just fine.
If you don't mind going in for a longer haul, I recommend Gundam Wing as a good starting point (50+ episodes if you count the movie/OVA Endless Waltz.) It is not set in the original UC timeline, but in its own timeline strictly for its series, so it acts as a complete stand-alone work while still keeping the "Gundam" feel to it.
I have not seen enough of Gundam Seed to pass judgment, and I have heard views of both loving it and hating it by people, so I really don't know either way on that one.