You want to beat the game with Heal Bellers, Hazers, Spikers, and precise natures? That's like, overkill... believe me, you'll be bored with the game soon enough if you try to go through it like that.
Also, if you're going to go through the game without doing precise EV-training, natures are going to matter squat to you in the long run. Just pick the first healthy-looking specimen that comes along to you.