Fear the Deer
Before I moved to Nuzlockes, I always chose my team based on what I felt like using. It didn't matter whether or not I had overlapping types. I mean, heck. My Pearl team has two ground types, both of whom have a 4x weakness to Ice. Now, with the release of a new generation, I normally went for a team consisting of new Pokemon for the initial playthroughs. After that, it was fair game.