I've thought about it some more...and I've decided that we already have a glimpse of the personalities of a lot of characters. Mario is shy but brave. Luigi is cowardly and usually just looks after the house while Mario is gone. Wario craves money and power. Peach is always in need of rescuing. Bowser is a pain. Baby Bowser is a pain too.
I was thinking that maybe we should see more of Professor Frankly (PM:TTYD), Professor Fungi (Mario Party 2), Daisy (Super Mario Land, MK:DD, MK:DS, Mario Parties 3 through 7, various sports), and Waluigi.