No other monster. Just Godzilla.
My preference is that this series is primarily Godzilla vs. Man. That's the central conflict that runs through the film and each successive sequel. It's what the series (back in G'54) was founded on: Godzilla vs. Man.
Man's Inherent Destructiveness is made manifest in the form of Godzilla. Now what can they do about it? That's
the story. That's the mythology.
While the other monsters won't be periphery characters, they will be there to serve as backdrop to this primary conflict.
Film 1: Godzilla vs. Man
Film 2: Godzilla vs. Man vs. Some Other Monster
or Mothra and Man vs. Godzilla
Film 3: Godzilla and Man and Mothra vs. King Ghidorah
Can you tell I've thought about this?