You know what , I know you cant just answer any type randomly but im gonna give it a shot .
These are the types :
Normal - Taken out by fighting .
Fire - Taken out by water .
Water - Electric .
Electric - Ground.
Grass- Fire
Ice-Fighting/Fire
Fighting-Flying
Poison-Ground
Ground-Water
Flying-Electric
Psychic-Dark/Bug/Ghost
Bug-Fire
Rock-Water
Ghost-Ghost/Dark
Dragon-Ice
Dark-Fighting .
Steel-Fighting
So the six pokemon that could take you through are :
Water
Fire
Fighting
Electric
Flying
Ice /Dragon
Maybe give them some moves of other types for coverage .
Types of moves other than their own:
Ground
Dark/Psychic/Bug/Ghost