A fire type would be a good fit here for the coverage, Maybe Pyroar/Ninetales/Magmar? I haven't played through the full game yet so I don't know what all fire types are available. Then you could pick one of the earlier picks, or not go with a fire type and pick both of them!
Hahaha thank you for the long post my friend! I've always had a quirk of raising a six-pokemon team and I don't want my types to overlap, just like you. Though I have to say I love the new look of the game. Feels so alive, I may end up raising more than six. It would certainly make the game last more:) I'll see what I'll come up with, thanks!!