Some Ideas i had:
Godzilla: Middle aged guy, works out a lot but looks fat no matter how much he works out, very grumpy, gets angry easily.
Mothra: Very old, kind, knows various forms of martial arts, probably one of the wisest of the Human-Kaiju
Battra: Mothra's twin brother(sister?), a lot nastier and more cruel
Rodan: Rival and Friend to Godzilla, two argue just for fun sometimes, very smart, not very strong, extremely fast though.
Anguirus: A bruiser, a bit dull, godzilla's best friend.
King Ghidorah: Doesn't like godzilla, but would prefer to be a pacifist, however, he gets manipulated by his friends into attacking him, as such, Godzilla hates his guts.
Keizer Ghidorah: King Ghidorah's father, hates godzilla, very strong and smart.
Grand King Ghidorah: Keizer's father, doesn't know much of anything anymore, too old to really care, hits on mothra occasionally, mothra really doesn't like him.
Death Ghidorah: Literally Satan, also Grand King Ghidorah's father.
Space Godzilla: Godzilla's brother, addicted to various drugs horribly, does steroids, a lot stronger than godzilla, but incredibly reliant on his addictions to stay living, possible pedophile.
Biollante: Godzilla's sister, went insane years ago due to issues with drug abuse forced upon her by her brother, attacks others regularly.
Gigan: One of Ghidorah's friends, brother of Megalon, known for his obsession with hurting and killing godzilla
Megalon: Gigan's brother, bullied by him to fight godzilla, really wishes he could stay away from this mess
Hedorah: Homeless, but ripped as hell, known for... unconventional.. fighting tactics, hates all other monsters
Minya: Godzilla's toddler son, has a severe mental disorder, kept in the house at all times, likes to play with insects.
Godzilla Jr.: Godzilla's older son, protective of his younger brother, could potentially be smarter and tougher than his dad one day.
Gamera: Godzilla's neighbor, who strives to be like godzilla, has his own host of issues to deal with, just as strong and smart as Godzilla, but more humble.
Gyaos: Completely insane, cannibalistic, kills others for the sake of killing, sworn enemy of Gamera.
Kiryu: Godzilla's father, on severe life support, has many prosthetic limbs and organs he is easily angered, and despite this, continues to fight if angered.
Jet Jaguar: Fan of superhero movies, knows martial arts, friend of godzilla, extremely kind.
Manda: Ghidorah's younger cousin, only person in his family who genuinely likes and respects godzilla., is shunned a lot.
Varan: Stunt pilot, Manda's best friend, known for being a daredevil.
Thats it for how i think they would be