Like in the first Dungeon game. Your Pokémon gets decided based upon based upon a personality quiz you get given at the start of the game. From this, the game determines the Pokémon you are. Once this has been decided, you can choose your partner.  

Pic: Name: Type 1 Type 2 Male Nature Female Nature
Bulbasaur Grass Poison Lonely Docile
Charmander Fire na Docile Brave
Squirtle Water na Quirky Bold
Pikachu Electric na Brave Hasty
Meowth Normal na Sassy Relaxed
Chikorita Grass na Calm Quiet
Cyndaquil Fire na Timid Calm
Totodile Water na Jolly Sassy
Treecko Grass na Quiet Hardy
Torchic Fire na Hardy Rash
Mudkip Water na Rash Lonely
Skitty Normal na Hasty Naive
Turtwig Grass na Bold Timid
Chimchar Fire na Naive Impish
Piplup Water na Impish Quirky
Munchlax Normal na Relaxed Jolly

However after that, you also get a choice of a Partner Pokémon. This Pokémon is decided based upon your main Pokémon. You get to choose out of the following Pokémon, cannot pick a Partner that is of the same type as your main Pokémon. For example if you get Piplup, you are unable to choose Squirtle, Totodile or Mudkip.

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