If you're looking for more serious-minded films in the series, it goes without saying that you should track down the original 1954 film and The Return of Godzilla. They all share the same setup (Godzilla on his own as a pure antagonistic force, focusing a lot on the human drama as they figure out how to respond to the threat), but go about it in their own ways. Those two are available on Blu-ray, though it needs to be said that the Criterion version of the original is the only way to go, as the other Blu-ray is a really crappy upscale of an older DVD.