Well if we want them to be a true rock-paper-scissors style group, each one needs to be strong against one and weak to another. So their types should reflect that.
Fighting/Rock/Flying works best for this IMO. You would think that Scissors might be steel, but Rock (rock) beats Scissors (steel) while steel type is strong against rock type. This is only if we want Rock to be rock type though. If the Rock was ground type, then scissors could be steel and paper could be ice. But having the rock be anything other than rock type doesn't work for me.
So Rock being rock, then flying scissors and fighting paper. I also think they should be just the single type.
Fighting/Rock/Flying works best for this IMO. You would think that Scissors might be steel, but Rock (rock) beats Scissors (steel) while steel type is strong against rock type. This is only if we want Rock to be rock type though. If the Rock was ground type, then scissors could be steel and paper could be ice. But having the rock be anything other than rock type doesn't work for me.
So Rock being rock, then flying scissors and fighting paper. I also think they should be just the single type.