This is such a personal choice, as many folks have opinions on what works where and under what conditions. All we can do is to tell you what to expect. Longer shots are always a fact of life when hunting in the west. It is not uncommon to get a 350-yard shot as the only chance you’ll get for a big elk or muley. So we encourage a flat shooting caliber such as a 270 or 7mm. It is not necessary to have big calibers to knock down an elk; a well-placed shot will drop them in their tracks. We always sight-in at 200 yards, this give us the most versatility. But in any case, the most important thing is to practice as many long shots as you can before you come. What is more important is spend the money on a box of premium bullets, e.g. Nosler Partition or Barnes Triple Shock. You want the bullet to do its job if it hits bone and too many bullets fragment which results in a poor, non-lethal hit.
Lion hunters: The cats will be treed, and shots won’t exceed 50 yards maximum. We typically aim for the esophagus. You not want to blow the animal apart. Many have used 22 pistols or 223 rifles, bows, cross bows, etc. It is best to check with is what you are thinking.