Hm...so much choices, so much types, so little to pick...anyway, here goes.
Normal: Sawsbuck, it has a unique typing, and a good distribution of moves and stats.
Psychic: Reuniclus, it can take hits, and can return with full force...it's also rather cute c:
Ghost: Either Chandelure or Gengar, they're both awesome in terms of design and looks.
Steel: Magnezone, its unique typing serves it a good purpose, as I recall it resisting a whopping 12 types.
Rock: Well, if it was legendaries included, Terrakion would have this spot, but since legendaries aren't allowed, I'll go with Aggron. Its one hell of a powerhouse.
Water: Gyarados - it looks menacing, has impressive strength, and it's always mad.
Poison: Crobat, it's really fast, looks like a boss, and has a good movepool - as I say: "Gotta go fast".
Grass: I don't use this type a lot, so I'll go with Breloom. Its Grass/Fighting typing wrecks most Pokemon competitively, and who doesn't love mushroom/kangaroo things?
Ground: Krookodile - its name makes me think of a hoodlum (I guess it's Scrafty's bestie), and..well, it's a crocodile.
Fire: Darmanitan, it's a flaming monkey thing, with fire eyebrows. Cool stuff.
Ice: Mamoswine is one of my fav Ice types, since it's strong, bulky, and Dawn has one.
Flying: Easily Staraptor. It outclasses the other starting birds in my opinion, and was one of my staple Pokemon during my Platinum replay.
Bug: Volcarona is my favourite Bug-type, since it's a giant flame moth, and is said to have been related to sun deities...
Dark: Weavile is a really cool Dark-type, and my pick here, since it's a cunning weasel with good power in its attacks.
Electric: This spot goes to either Rotom or Jolteon...Rotom is a versatile Pokemon, as it has its different forms, my personal favourite being Wash Rotom. Jolteon's a fast, powerful and cool Pokemon, which served a main purpose during my first Platinum playthrough.
Dragon: The Hackersaurus! Haxorus is definitely a beastly Dragon-type, strong, and looking like a menacing Dragon-type (look at dem tusks), something you don't want to mess with.