Mario is the first character you have. You always have to have him in your party. You'll want him along anyway.
You meet Mallow in Mushroom Kingdom. He becomes a member of your team after you agree to help him get back his grandfather's frog coin. In our opinion his only good attack is his Thunderbolt. When you get later characters, its probably best to opt for someone else.
Geno is the coolest character in the game. He has the coolest and most powerful attacks. He helps you on your quest for the Star Pieces. I would always keep him in my party.
Bowser is a powerful ally early in the game. In past Mario games Bowser has been the enemy. This may be the only game with him as a friend. Put his largeness to good use.
Princess is the other party member I would always keep when fighting bosses. Her healing powers are unparalleled to anything else. Keep her defense high.