I go for usually what is strong and at the same time cool looking, but I value inner strength and beauty more so I definitely go for "strong" pokemon.
Most of the time, i would just say the easiest things and say I'll just go with what i like: Blaziken, Gyarados, Garchomp, Gardevoir, Excadrill, Metagross and there I'm done, but then again, that team as much as they are cool looking and badass, is still pretty shitty competitive-wise because its all hyper offense with no utility so its a really predictable team. But I love them all anyway and all of those pokemon i mentioned are great pieces for certain competitive teams that can be built around them.
But then again, when i know that a Pokemon can be strong because of its capabilities, then i go for it. Most people would say Crustle is a shitty pokemon because it looks like a brown piece of cake but then they don't see how good a Shell Smash Crustle can be. Then there's Chincinno from Unova. Oh its a cute little bunny that most girls would just keep as a pet and don't bother fighting with it, then they forget that Chincinno can have Skill Link for its ability, the same ability that makes Cloyster one of the most feared pokemon in the game right now, and it actually kicks a lot of ass. I have a Chincinno in my White 2 party and its kicking a lot of ass with those always 5-hit Crit Tail slaps. And of course there's Cloyster a pokemon that i thought was always cool but was never any good in most of the past generations until it got Skill Link because as i mentioned earlier, Shell Smash + Sash + Skill Link Cloyster is such a cheesy monster that it makes me feel bad watching someone get swept by it. And then there's Jumpluff. Oh its so cute, its obviously not a threat. Its so cute that people would laugh at me for having such a weakass pokemon with me. WRONG. Jumpluff is such a great pokemon that not a lot of people realize who threatening it can be with the right moves and right teammates to work with. Jumpluff is a threat.
In short, if its cute, its cute. If its cute that can kick a lot of ass, like Jumpluff, Chincinno, Crustle and the like, then i'd use it.
And then of course there's this question:
do you guys believe you can make it through in game using any pokemon regardless of typing or stats? Or do you believe balance and strength is necessary?
My opinion is that well, I don't want to. Its possible to go through the games with some of the most subpar of pokemon, and there's even those people who deliberately not let their pokemon evolve as well, but I'm just not one of them. I remember in those good ol times with Pokemon Yellow that I never had the heart to dump that starter pikachu because i got emotionally attached to it, even though its stuck with subpar stats compared to the rest of the good ones that I had with my Yellow team such as Blastoise, Charizard, Nidoking, and Ice Beam Chansey. I held on with that Pikachu but its stats were just too low to handle even the Elite Four part of the game, but at least it can still hang on against Lorelei's Water/Ice types. But having to use potions for Pikachu every time it failed to KO a threat and it taking a chunk of damage in return made me realize that i just can't handle playing with subpar pokemon when it comes to tackling the end-game.
Sometimes you need the strongest or at least the most workable pokemon to not make the journey frustrating and the battles irritating. Its not just for the sake of winning but its also for the sake of having fun as well. Its great to have some oddballs in the party and not just those super good OU and Ubers to basically just insta-win the game, but some oddballs still have to be actually good in order for me to have fun. So its in the matter of being good and at the very least, "not sucking".