I'm going with Heisei on this one. The characterization of Godzilla was perfect. And, like MouthForWar, I too had been well-aware of the Heisei Godzilla movies as they were coming out. It's true, they all looked virtually the same in terms of production values, and special effects and so-forth, but that was the cool think about them for this nine-year-old at the time. I was still impressionable enough at the time, that these movies had no problem soaking themselves into my memory-bank. I watch them today, and yes, I do acknowledge their technical short-comings, but I just have to give them the benefit of the doubt here. To me, the Heisei Godzilla series got just enough right, insofar as the Godzilla mythology is concerned, that I have no problem referring to it as "the Second series". Second, of course to the Showa era, but you knew that already

Plus, it has Akira Ifukube, and that pretty-much clinches it for me!
No disrespect to the Millennium flicks, however. I like them too. I think that
Godzilla Mothra King Ghidorah: Giant Monsters All Out Attack is probably one of the best Godzilla films ever made. But on the whole, I prefer the best of the Heisei series to those of Millennium...
Godzilla vs. King Ghidorah
Godzilla vs. Mechagodzilla (1993)
Godzilla Mothra King Ghidorah: Giant Monsters All Out Attack
Godzilla vs. Biollante
Godzilla X Mechagodzilla
Godzilla 2000 Millennium
Godzilla X Megaguirus
Godzilla 1985
Godzilla vs. Mothra
Godzilla vs. Destroyah
Godzilla vs. Spacegodzilla
Tokyo SOS
Godzilla Final Wars
"EVERYONE FORGET YOUR TROUBLES! ENJOY YOURSELVES!THERE'S NOTHING TO WORRY ABOUT!" - Gigantis The Fire Monster
"It was HUGE...It was...IT WAS LIKE A MONSTER!!! Suddenly the rocks rose...ALIVE!" - Godzilla 1985