I watched the original Godzilla, and I found that it was much more serious than I expected. From what I've seen from clips and plot summaries of the later movies (and watching the 2004 Godzilla: Final Wars movie), they're nothing like the original. It seems as though the Godzilla series basically breaks down into the original on the one hand, and the rest of the series in a quite distant and much sillier other hand.
I'd like to give Kaiju films a shot, and I like that they're something unlike anything I've seen before, but Final Wars was too empty (terrible script, not much plot, and IMO uninteresting action scenes), and the original Godzilla was really just an anti-nuclear disaster movie, not a fantasy action film.
But there's like 50 million Godzilla films (not to mention all the other Kaiju movies). Where to start? Maybe just Godzilla 2?