Hi! :D
Hahaha, I totally know how that feels. I usually just end up picking my favorites because I can simply level-grind or recruit more Pokémon to make up for any disadvantages within my team. If Shinx is your favorite Pokémon, then I'd say go for it! However, I might recommend choosing either Riolu, Charmander or any Grass- or Water-types to be your partner, since they can provide some pretty decent coverage. Oh, and don't forget to feed your Pokémon plenty of Gummis, since those are essential to getting stronger!
Best of luck, and I hope everything works out!