My first elk was killed with a 7mag at 80 yds. Lung shot, sucking chest wound, put a second shot in 2 inches from the first. The bull trotted up and passed me at about 10 yards, went another 20 yards into a copse of trees, where I heard him walking in circles while his lungs filled, then he fell over. Took about 5 minutes. I got a 338mag to put some more "authority" on the subject. With 225 and 250 Noslers that gun has dropped 5 elk cleanly at between 40 and 400 yards, none went more than 10 yards from impact. One, at 325 yards, I put a second shot into because his knee only twitched at first impact. Both shots went into the lung cavity and were killing shots. My last two elk have been with a 300 Win mag shooting Nosler 200's in the Federal High Energy load (no longer manufactured). Just as much "authority" as the 338.
My conclusions after 20 years: 1. Use as much gun as you can comfortably handle. 2. Use a gun and load you have confidence in, even if the confidence is subjective rather than objective, 3. Shoot target pistol to learn trigger control and avoid flinching, 4. Use a PAST recoil reducer for sighting in at the range. You can shoot 5 or 10 shots or more without getting a sore shoulder and starting to flinch. 5. For any shot over 300 yards estimated, use a laser rangefinder and memorize your load's trajectory out to 500 yards. If you don't have time to use it, don't take the shot. 6. If you want to drop an animal in its tracks every time, you have to break the spine or shoulder. A heart/lung shot, with any caliber, usually, but not always, takes a little time. Good hunting to you.