A friend of mine once called me a Pokermon Hipster, and when they told me why, I kind of accepted the title.
I love pokemon that have incredibly unique move pools that encourage combo design, and on top of that I enjoy taking pokemon that are commonly disliked and attempt to make viable builds for them. I also prefer to not use pokemon that are obviously overpowered. I was called a Pokemon hipster because I think unpopular pokemon are really cool.
I will admit, from a visual design perspective, I tend to gravitate towards the cuter pokemon, but it's not anywhere near the main factor that decides whether I like a pokemon or not, and how often I will use it or pick it for my team.
I prefer unique stats, I don't mean powerful stats, I like pokemon with stats like "Ninjask", "Steelix", "Shuckle", for example, their stats are not top tier, but they're focused towards specific niches, and designing a pokemon to truly take full advantage of that unique stat makes that pokemon pretty interesting to me.
Another factor that helps me decide what pokemon I find interesting, is their overall collective move pool, which includes the moves they learn from basic level up, the moves the pokemon has access to through, breeding, tutoring, TMing, HMing, and any other fields of attacks that pokemon may have access to. I like reading through the collective list of moves pokemon have access to, and I will try to search for moves that naturally combo into one another that is unique to that pokemon, or at least a rare movement build that is only shared by a few pokemon. I enjoy using "Chimecho", "Jumpluff", and "Lickilicky", because they have unique move pool collections that have moves that interestingly combo into one another. Their stats may not be impressive, but their movepools, make up for their lack in powerful stats, and the fact that the combination of specific moves they can do aren't shared by any other pokemon, makes them attractive choices to me.
The very last factor that determines my interest in a pokemon, how popular is it. That may sound shallow, but it's the pokemon that are used by everyone or that are obviously in your face powerful, are the pokemon I prefer to stay away from. When I used to play online or with friends, I was just tired of seeing the same pokemon over and over again, and the pokemon that were used over and over again, they were only picked because obviously powerful pokemon are obviously powerful. Just seeing the same old teams over and over again broke the interest of playing the really powerful pokemon. So I found more fun in looking at alternative pokemon, pokemon that were commonly ignored but were still perfectly viable for playing competitively if raised properly and built with move pools that are rock solid for any kind of battling situation. I also can not begin to explain the delight I feel when somebody makes fun of one of my weird pokemon and then it just totally kicks their butt, best feeling ever.
I'm a bit of a weirdo when it comes to what pokemon I like and how I judge them, but it hasn't made me a bad team yet, and a few of my pokemon playing friends have even copied a few of my weird pokemon builds, so I must be doing something right.