The cheap Federal ammo "Hi Shok" or "PowerShok" in 180 grain will have no problems dispatching deer, elk, moose, black bear, etc...
I put a 180 grain from my .30-06 through the hip of a large muley. After a mad 30 yard dash, he went down. I recovered the bullet from the skin on the far side. It was a perfect mushroom, retaining much of its weight. No I did not weigh it. My dad and I were both surprised at the bullets performance as it was thought to be a rapid expansion 'shocking' bullet. It is all my dad takes into the now with confidence for bear, moose, deer and elk.
I am like you probably. I like to roll my own and I like to use 'premium' bullets. Why not try to minimize any factor that may lead to a lost animal. Like you said, your skills are not the issue. Buy a box of a couple of different 'premium' bullets and use the one that flies the most consistently.