1. Showa - a diverse selection of films, many of which are classics. The original film stands alone as a rare gem, and everything made from 1964 to 1968 is the gold standard for a lighter, more absurd Godzilla that still delivered good stories and action.
2. Heisei - the 80's films have plenty of faults, but they're both quite ambitious, especially Godzilla vs. Biollante's intricate plotting. They also have great atmosphere, and Godzilla is genuinely intimidating. Godzilla vs. King Ghidorah kept *some* of this magic going, but then Godzilla vs. Mothra just killed the momentum and the series never really recovered. Still, there's a lot to love here, including what I still think of as the definitive version of Godzilla.
3. Millennium - Big old mess, though I do like the human drama in Godzilla Against Mechagodzilla (if anything it should have been fleshed out more); the first half of GMK is excellent; and the US version of Godzilla 2000 is a good time. Otherwise, I give these movies a wide berth.
4. Monsterverse - ...man, I almost forgot I had to list this. They're all stellar productions, but they mostly failed to live up to their potential with the storytelling. Pretty weak scripts overall.