Wow! This is an exceptionally well thought-out question!
My preference tends to involve pokemon hardly seen in competitive play, or even at all. It helps to have unevolved pokmeon, as long as they can still put up a decent fight. (For example, I have a pretty decent Hippopotas in my party that can take a lot of hits and deal lots of damage, but that's only for Pearl & PBR ingame battling, so I'm not sure whether or not it counts.) I do think that all the other elements of competitive battle also matter, like a pokemon's stats and movepool. However, even if you take the supposive best pokemon in that aspect, there's always going to be something that can take it down. Knowing that, I just stick to what I like, and do the best that I can with it, no matter how long it takes (even if I have to train a pokemon almost to Lv50 for an egg move, breed for a Pichu, evolve it, and then breed for another one afterwards, which is what I've been doing at the moment).
Summary: Anything can be stopped, no matter how powerful, so try to go for something unique to you and no one else.