Let's say you are hunting for elk sized and smaller game and are targeting 750 yards or less.
So many calibers out there, I just want to start with the right base and get proficient from there.
Do I enter this minefield? Elk-sized and smaller game includes a lot of different sized game animals. And 750 yards back to the muzzle also covers a lot of ground.
I believe you're primarily focused on the selection of an optimal caliber rifle for your needs. Since you included elk on out to 750 yards in your criteria, you should pay heed to Broz's experiences, and lean toward at least a 30 caliber. If it's just an occasional elk hunt and more deer-size game hunting, buy a 30 caliber magnum rifle and install a muzzle brake or suppressor on it.
Then when you hunt elk, research bullets further and select a good one. There are countless threads covering bullets and bullet preferences on this Forum. A single brand and style of bullet that covers all shot scenarios best is like searching for the pot of gold at the end of the rainbow. Some bullets are better for certain challenges, tasks, and situations, than others.
The reason this discussion so quickly turns to the best bullets for the job by very experienced hunters, is because bullet construction and performance plays such an overwhelming role in how quickly, consistently, and reliably, a game animal is killed. And even these bullet criteria can change, when attempting to address all of the various calibers and weights of bullets, the different sized game animals, across the spectrum of shot distances.
I still prefer the selection and use of two bullets. One bullet is for game animals that don't come equipped with teeth, fangs, and claws and the high propensity to maim or kill me - and is selected with the focus on long distance shots. This bullet has to shoot very accurately out of my rifle to make good hits at long distances.
The second bullet is for dangerous game and non-dangerous game at closer ranges. Say from the muzzle out to ~350yds. The primary focus on this bullet is reliability of terminal performance inside the animal. This is the bullet I'm betting my life on in short range encounters with bears or any other game animal that might try to kill me. This bullet is also a great performer on non-dangerous game out to ~350yds, killing quickly and normally with less bullet-caused meat damage than my long range bullet would at the closer ranges. Accuracy is a minor consideration when selecting this second bullet, because almost any decent bullet out of any decent rifle is accurate enough to kill deer-sized game at these closer ranges.