Ok, quick overview: Gundam has several different timelines, grouped broadly into UC (Universal Century) and AU
(Alternate Universe). The main UC series are the original MSG, Zeta Gundam, ZZ Gundam, Char's Counterattack, and V
Gundam. UC sidestories include 0080: War in a Pocket, 08th MS Team, 0083: Stardust Memories, and F91 Gundam.
There's also a couple of manga additions, most notably Crossbone Gundam. The AU series are Gundam X, Gundam Wing, G
Gundam, Turn A Gundam, and Gundam SEED/Destiny.
Starting with the original is never a bad idea; however, rather than the series, go for the compilation movies, which
replace the series in canon IIRC. After MSG comes Zeta, which many people consider to be the best Gundam series of them
all. A boxset was recently released for Zeta as well, if you buy legit stuff. The problem with the UC timeline is that
it's huge, and requires a considerable investment of both time and money. ZZ and up haven't been licensed or
released in the US (with the exception of Char's Counterattack, a movie). F91 was planned for a full series, but
was cut short to a movie. By the time V Gundam rolled around, the UC series weren't connected at all (as opposed to
MSG, Z, ZZ, and CCA, all of which have directly connected), so much so that V felt like an AU anyway.
The AUs are nice in that they are all independent, with the exception of Gundam SEED and SEED Destiny. SEED starts off
pretty weakly, feeling a bit like a retelling of the original Gundam, but ends rather well. Destiny is the opposite,
starting out incredibly well but falling flat on its face in the last 10 or so episodes. Gundam Wing is a nice place to
start. G Gundam is rather different from the other series in that it is a super robot show, rather than a real robot
one. Expect cheesy dialogue, shouting attacks, and hot blood. In short, G Gundam has more in common with GaoGaiGar than
it does with Zeta Gundam. I'm personally watching Gundam X at the moment, and am loving it.
Turn A is a different beast altogether. This was Tomino's attempt to link the various Gundam universes, and it
spawned the 'Turn A Bang' theory, which places UC and AU series in a direct timeline. Some people don't
accept the theory, though. Furthermore, Turn A has by far the strangest designs, and is much more character driven than
the other Gundams.
So, I'd say start with the MSG compilation movies, then go for some OYW sidestories, namely 08th MS Team and 0080,
both of which are great series. Then Zeta if you want to continue UC, or Gundam Wing or G Gundam.