My favourite Pokémon, for instance, is Celebi. In battle, it can hold ground with Leech Seed and Nasty Plot, maybe, but it has a whopping seven weaknesses, having the most number of weaknesses in the game. But, I quite like it's design and the "foresty" and natural feel it presides, just like Xerneas, and that design soothes me. I quite think that it's typing is better as Grass/Fairy, though. But more of that later. This shows that I go for design and the little-cute-little-cool type of Pokémon.
But, I like Swampert as well, or Mudkip to be exact, and that closely follows Celebi, much because I like all Hoenn Pokémon and Water and Ground types. This means that typing means a lot to me too, whether it be crippling or not.
But like quite a few before me have said, I get chosen by my favourite Pokémon. This also means that I don't gradually grow to like a certain Pokémon, it's at first sight my final judgement is made.