Reddit reviews A Critical History and Filmography of Toho's Godzilla Series, 2d ed.

https://www.amazon.com/Ishiro-Honda-Life-Godzilla-Kurosawa-ebook/dp/B0788KLDK9/ref=sr_1_1?s=digital-text&ie=UTF8&qid=1538082752&sr=1-1

https://www.amazon.com/Eiji-Tsuburaya-Monsters-Defending-Ultraman/dp/1452135398/ref=sr_1_4?s=books&ie=UTF8&qid=1538082718&sr=1-4

https://www.amazon.com/Critical-History-Filmography-Tohos-Godzilla/dp/1476672946/ref=sr_1_10?s=books&ie=UTF8&qid=1538082718&sr=1-10

https://www.amazon.com/Japans-Favorite-Mon-Star-Unauthorized-Biography/dp/1550223488/ref=sr_1_2?s=books&ie=UTF8&qid=1538082734&sr=1-2

These are basically the best books on the series that are easily available, although the Tsuburaya book is really about the effects. As for the 3 films that really capture the original theme of the series, I'd say the original, Mothra vs Godzilla, and GMK are the ones that really hold the most important messages. All three of these were made by pacifist directors who renounce war and the actions of imperial Japan. The original Godzilla is an anti-war film, period. Mothra vs Godzilla is about harmony between nations. GMK is about keeping the past military actions in mind, in a modern Japan which is whitewashing it's war crimes out of history. Some people might say Godzilla 1984 and Shin Godzilla carry similar messages, but 1984 is more about the height of the cold war and Japan's place in it while Shin is about the need for a stronger, fast-acting independent government. Similar themes, but they're not really tied to the original as much as Mothra vs Godzilla or GMK.

Here is "A Critical History and Filmography of Toho's Godzilla Series" by David Kalat. It's a good read that may help out a bit with you research.

As for my personal thoughts? Godzilla is a character which can be applied to a variety of metaphorical situations in which Humans are shown not to be as in control of their environment as they'd like to believe. It lends itself well to films on the human condition. People love stories about the weird, unusual, and monstrous, while also subtly analyzing the inherit complexities of what is means to live in conjunction with our environment. As such, Godzilla films have the ability to tick those boxes. People love to watch monsters fight eachother. It gives them the adrenaline rush and allows them to feel like something bigger than themselves is on their side. So that box also gets ticked pretty frequently.