I've watched so many anime that I'm not even sure who my favorite character is anymore, so I'm going with one of my original favorite characters as well as my namesake when I first joined PC back in the day: Koga (Inuyasha).
I'd give the leader of the wolf demon tribe a Midday Lycanroc as a general representation of wolves, as well as Manectric for the Goraishi, the lightning claws that fused with him in the Final Act. Maybe Lucario, a Steel-type lupine, with the egg moves Vacuum Wave and High Jump Kick. Koga's name means "iron fang," his inhuman speed is accelerated by vacuum waves, and he's often seen fighting with his powerful legs.
EDIT: In terms of favorite
human character, a few that come to mind include Kyo from Fruits Basket, Kanata from Daa! Daa! Daa! (UFO Baby), and that lovable idiot Kana from Minami-ke.
Kyo would obviously have a cat, probably Litten. I could also see him with a Tyrogue or one of its evolutions since he trains in martial arts. As for the other two... I guess Kanata (along with Miyu) could have a Cleffa to represent baby Ruu, and maybe Meowth to represent the talking, cat-like sitter-pet, Wanya. It's been several years, so I'd have to rewatch the series for any more ideas. Kana would have a Heracross based on her pet rhinoceros beetle, though I could also see her with Psyduck and Bibarel (dummies), Scrafty (SHE IS BOSS), Steenee (pigtails, middle sister), and Furret (similar faces) if she had a team of six.