With the exception of Godzilla and Godzilla x Biollante, they have the entire Heisei period. It goes in order of Godzilla X Ghidorah, then Mothra, then MechaGodzilla, then Space Godzilla, and finally Destroyah. If you want to watch a bunch of films with continuity, Heisei is for you, as each film builds off the last. I kind of have a love/hate view of this particular era. One the one hand, the character designs for the suits are very detailed and the monsters look amazing for the most part. Unfortunately, because of the size and complexity of some of the suits, they're not as animated as in other eras. For example, in Godzilla x Ghidorah, you'll never see Ghidorah walking. The "science" behind a lot of the stories is shoddy as heck. Time travel, genetics, nuclear energy. Ugh. It's bad.
Then again, scientific accuracy was never a big concern. Kind of like the special effects. Sometimes they're embarassingly bad, even in the more recent Millenium series. But I think, maybe that's the charm, because everybody who makes these films cares much more about telling the stories first and visual realism comes second. It adds to the charm of these movies. Dubs take away. I don't know about the others, but at least for the Heisei films I'm gonna jump through today, they all seem to be TriStars releases, so there's no Japanese voice track available.
Know what I've never seen? The Rebirth of Mothra trilogy. I like Mothra. I should get my hands on a copy of that shit.
Realism. You want unrealistic and campy, that's what the Showa era is for. For the most part, it's all men in rubber suits pulling off pro-wrestling moves on each other. It's freaking awesome. Godzilla x Megalon is a personal favorite of mine. You got Godzilla and Jet Jaguar (an Ultra-Man Rip Off) beating the crap out of Megalon, a giant cockroach from an ancient undersea society, and Gigan, a space-cyborg monster with freaking scythes for hands.
If you only have a passing interest in Godzilla and wanna check him out, I'd recommend almost anything from the Millenium Era. With the exception of Godzilla Against MechaGodzilla and Tokyo S.O.S., there's no continuity, so each film is a stand alone. Godzilla 2000 is probably the best. Don't watch Megagurius, it's beyond awful. Probably the only one worse than that is Godzilla Raids Again. Unless watching two hand puppets pretend to bite each other is your thing, then totally watch Godzilla Raids Again.
I still haven't seen Shin Godzilla. I need to get a copy of that. I hear it's a trip.
Legendary Godzilla was cool too.