Showa Godzilla vs Mothra is one of the better entries in the series, for sure. Granted, Godzilla loses to the Mothra Always Wins rule, but it's got mostly solid effects, and the storyline has some pretty scathing commentary on political and commercial exploitation mixed in with the giant monster on the loose plot. It's got one of the better strong female roles in the series, and I also consider this the first movie where Godzilla is portrayed more like a force of nature or a creature born out of time, rather than just a malevolent destructive being.
All that being said, of the Heisei films, Biollante is probably the best jumping-on film. It shows pretty much everything you need to know from Godzilla 1984 right at the start, and then builds on the world from there. It definitely leans more into sci-fi tech than Godzilla vs Mothra, but mostly within a believable level (again, building on the scenes from 1984). The effects are also very solid, with some pretty spectacular moments here and there.
TLDR, I don't think you could go wrong with either of these.