I usually use the Pokemon I have used in game and love. I know they're a bunch of pixels and aren't real but it has a deeper meaning for me, I don't want my Pokemon to be a bunch of numbers, society nowadays is now fixated on qualifications and I hate that, it makes it out to be that you are a nobody if you don't have amazing grades.
But I do sometimes if I'm breeding a team I'll focus more on the nature and EVs then so much time on IVs. But I rarely use perfect IV Pokemon, if I'm given one then hell yeah.
I may be awful in competitive single battling because of this but I much prefer rotation battles, so much more fun seeing what type of person you're battling, arranging the perfect team and predicting what they'll do next.
But I'm usually pretty happy with the Pokemon I spend my journey with, I all ways keep them, even if they have a bad nature or such.
If I was to go into tournaments I may have to IV breed Pokemon, but I usually prefer move pools and typing over that. Of course I won't use utterly weak Pokemon, even if I find them cool or cute, but thankfully with Amie and in the past with competitions and the Pokeathlon those weaker Pokemon because more valuable.