Will: Dark/Ghost should beat everything.
Koga: Psychic should beat most things, Fire is good also for Ariados and Fortress.
Bruno: Flying/Psychic/Fairy should beat mostly everything, Water/Grass for Onix.
Karen: Fighting/Fairy should beat more than half her team, Psychic for Gengar and Vileplume.
Lance: Rock is a good type here because everything in Lance's team is part Flying. Electric will likely one-shot Lance's lead Gyarados, and can do decent damage against Charizard and Aerodactyl. Water works well on both Aerodactyl and Charizard. Ice/Dragon can give you an edge over the Dragonites.
Just my opinion though.