What others have said, 1954 is essential. Dated perhaps, but the exploration into the pain of a nation that has witnessed the horrors of the atom bomb is unique to this film, and it matches the looming dread of Minus One and Shin. Godzilla's destruction of Tokyo is arguably my favorite scene in the franchise.
After that, it's really your choice. GMK, vs. Mechagodzilla (1974), Mothra vs Godzilla (1964) are all strong movies. Do note that ever single Showa movie has a musical scene. I don't know why, but it is what it is. Sometimes they're actually sick bops like King Kong vs. Godzilla and Ebirah Horror of the Deep, and sometimes they go on for four minutes too long and grind the movie to a halt like in Mechagodzilla 1974.
Still more lively than most Heisei films though. If you want to check those, I do unironically recommend vs. SpaceGodzilla. It may be nostalgia but the characters work here, and the plot is bonkers enough to fall in love with.
If you're going to watch Godzilla on drugs however, you should definitely watch Godzilla vs Hedorah. Greatest movie of all time while tripping.