The main thing I go for is type balance. I try to avoid having more than two Pokemon with the same weakness on one team, for example Ground, Grass and Flying together because they're all weak to ice, or Flying, Bug and Fire together because they're all weak to Rock. My favourite types are Water, Flying, Fire, Electric, Psychic, Grass, Ice and Ground, so I usually go for those types.
Another important factor is stats. I try to have a good attacker, a good defender, a good special attacker etc. and I usually don't like having more than two of each on a team, so I wouldn't have three special attackers and only one physical attacker. I'm also more inclined to go for Pokemon that have high defence, special defence or HP, because I hate it when one of my dudes is OHKO'd by a strong attack that isn't even super-effective.
As for nitpicky things that don't actually matter in-game, I prefer Pokemon that are based on animals rather than inanimate objects or supernatural things, but I wouldn't say no to an awesome one like Magnemite or Baltoy. I'm also fussy with genders, I don't like having an all-male or all-female team, and if a Pokemon looks particularly feminine (like Roselia) I'll try to get a female, or particularly masculine (like Heracross or Pinsir) I'll try to get a male.