Whoops. I guess it was 2 years ago Darkowl asked for the best film. A bit late, but here’s my list:
Godzilla
Godzilla vs. Mothra (aka Godzilla vs The Thing)
The Terror of Mechagodzilla
Godzilla, Mothra and King Ghidorah: Giant Monsters All Out Attack
Godzilla: Tokyo SOS
I would suggest watching them in the original Japanese, especially the first film which was heavily re-edited. We own and enjoy them all (at least the 28 films up to the current series). These days most everything is available in beautiful Blu-ray or DVD copies with both original and dubbed versions
There are three different periods of production not counting the modern films:
Shōwa period (1954–1975)
Heisei period (1984–1995)
Millennium period (1999–2004)
Don’t forget there’s lots of other great kaiju eiga films besides Godzilla; War of the Gargantuas leaps to mind.
And it looks like Criterion now has distribution rights for many of them:
https://bloody-disgusting.com/home-video/3469049/criterion-collection-obtained-showa-era-godzilla-films/