My favorite of those listed would be the Winchester Power Point. Remington core Lokts would be my last choice.
It makes sense to go with the heavier 180 grain bullet when using the "non-premium" bullets. The heavier bullet is slower, and speed is what causes cheap bullets to disintegrate, so it should stay together better than a lighter, faster bullet.
The 30/06 with a 180 grain bullet is classic. You just can't go wrong with that combination. Good for deer, bear, elk, and everything else, whatever that may be.