Before defeating the Elite Four, I carry the pokemon that are found in the beginning areas of the game, depending on the version. I find it easier to catch pokemon for my team at the beginning of the game and start training them from there then wait for a specific pokemon later in the game. I also almost always have a "Team Leader". The team leader is always at a higher level than the other pokemon, making them the most used and trained of my team. I do this because I'm just so eager to fight the Elite Four and the fastest way to do that for me is to have a team leader.
After the Elite Four, I normally carry one high leveled pokemon following the pokemon I need to train (Not a team leader because I never battle with the pokemon unless I have to.) This provides extra safety when I'm training. What kind of pokemon do I carry? Just about any pokemon, however, I almost never go anywhere without the company of my Vaporeon. Primeape has also grown on me as well.
I bring my pokemon's true potential out by selecting the pokemon it goes against before-hand by determining the EVs it gives. Once we set out, I make sure I have plenty of medicine with me as things may get rough. I try to avoid the fainting of my pokemon at all costs.
Once I'm done with the EV training, I'll start training them for exp. The Lucky Egg serves good use for this, as well as the Elite Four and Audino (B&W)
I suppose I'm one who trains their pokemon individually, rather than a team. I'm not sure if it's a positive or negative thing but that's my style.
