This would be my core list. They're all really good options in my opinion and none of them are that hard to track down, with the exception of the Gamera Trilogy which is sadly out of print at the moment. I really hope it gets re-released soon cause I've heard so many good things about it. What did you think of Pacific Rim and Godzilla '98?
I think I'll carve some time out this week for Godzilla '54, since my gut reaction is to go with an absolute classic and build out my understanding of the genre from there! That list reminds me: I've seen Cloverfield, but it's been so long that I can hardly remember all of the details. I remember wishing for more "BIG MONSTER SCARY" and less "College kids can't communicate well!" Pacific Rim is just good fun. I loved the big battles, and I really enjoyed how it was shot (mostly) from a human perspective. They do a great job selling the scale of the battles, and I think the score is perfect. Godzilla '98 was a long, long time ago. I liked it as a kid, but having seen footage of it with adult eyes? Meh. I think it's a bit schlocky, but I'm coming at that with a pretty heavy bias built from years of exposure to people who hate that movie - maybe I'd like it if I gave it a second chance, but there are so many great movies I haven't seen. I'd rather take a risk on something new!
Godzilla '54 is a great start. It's dark and serious, so it doesn't match the tone of the rest of the Showa era, but it's pretty powerful. If I could expand on that just a bit, not that you have to watch these films, but just to talk about the evolution of the era a bit. The next film in the series is Godzilla Raids Again and due to a rushed production, it's a bit of a flawed film. However, it lays down some groundwork for future vs. films. The third film in the series is King Kong v Godzilla and this is where Godzilla becomes more of a colorful character and we the series take a tonal shift into being action and adventure oriented. The fifth film in the series, Ghidorah the Three Headed Monster is where we see Godzilla first take on a hero role and on the series evolves from there. There are some really good resources about Godzilla's history that I'm learning a lot from. I think pretty soon I'm gonna make a thread about what I've been reading and watching, because obviously none of this I'm learning through conducting my own research and there's tons of good stuff out there. Besides, credit should be given where credit is due. :) I only watch Cloverfield once every few years, but each time I take away something new from it. I can promise you the heroes aren't as annoying as you remember. At least, I kind of like them. :) The only thing about that film that I don't like is that the filmmakers put in a couple of scenes and images that are reminiscent of 9/11 and I'll definitely go over that when I get around to reviewing it because I definitely have opinions on the matter. I will personally say that each time I've seen the film, I've liked those scenes less and less. That said, they do such an amazing job with so many other things, it's still a great piece. I totally agree with you on Pacific Rim. It's just a treat. I haven't seen that film in years, but I recently rewatched the Cinema Wins video for it and it reminded me of so many reasons of why I like that movie. I'm not as personally as generous in my views towards it, but that doesn't mean I don't find it just delightful. As for Godzilla '98, it's honestly not as bad as people make it out to be. If it had come out under a different title, it probably would have been better received. For tons of obvious reasons though, it just doesn't live up to the public perception of Godzilla or his legacy. All that aside, it still has quite a few flaws, but viewed as an experiment, it's an interesting piece.