Yes well I think the rest is down to us as of now. Like Gray said, it should change over the journey, and not just Crono's personality.
General Outline of Personalities:
Crono: Punk, Rebel etc.
Marle: Also a Rebel yet pretty in that funny sort of way
Lucca: Bloody genius
Robo: Too nice for his own good. Would be a martyr if the case arrived.
Frog: Courageous, Brave, a bit Suicidal, probably a ladies man
Ayla: Likes to beat the living shit out of things, wat more can I say.
Magus: The ass-wooper of the group, quiet, mystical, mysterious, thinks of the rest of the crew as a burden.
Take this as a conceptional framework to the personalities.
Im also trying to see if this Project is still running.