The Gems and their Pokemon! I love how they portray their personalities and their capabilities are similar to these Pokemon. Manaphy perfectly fits Lapis, like how they just want to go home and Arcanine reminds me of Lion.
Dipper, Mabel, and Bill - Gravity Falls and Pokemon Hmmm actually I think Dipper and Mabel would choose not a type but rather a theme. Bill perhaps too but a Psychic-Dark combo sounds good for him too.