Most of the cartriges mentioned already will perform adequately, but it is ultimately the rifle that dictates accuracy.
You should strive for a top-quality bolt action that is built for accuracy, and that means custom, not off the shelf.
Then you need to work up the best-performing handload for that particular rifle.
This is assuming that you can do your part, which usually takes considerable practice.
As far as taking a large animal, I don't know why anyone would take a target rifle out in the weather and subject it to casual handling.
Well, this is all a learning experience for me which is why I ask for advice from you all. I don’t handle any of my firearms in a casual manner. I am unsure whether I will be swapping out the stock but I know I may have to upgrade some parts to get what I want. I am working on doing my part.