A 9.3x62 sounds like it might be an obsolete military round. That's .366 caliber, which is a fairly strange bird.
FB3, I'm not sure what you mean by saying that the .30-06 "does not have many choices as far as loads and bullets go". As you noted, the .30-06 is a ".30 caliber" round. That means it will take any .308 bullet you can get your hands on. It's a bottle-neck case, meaning it will live happily with a wide variety of powders. So the choice in handloads is immense. For off-the-shelf ammo, Winchester and Remington both offer 16 different loads. By contrast, the majors offer six or eight different loads for the popular .300 Winchester Magnum. The .30-06 is, rather than being limited, perhaps the most versatile of all rifle calibers.
Except for the 9.3 round, none of the cartridges you listed would be a bad choice, Skunkabilly. I might fudge a little on the .338, since that is more gun than is necessary for game the size of deer, black bear, or smaller stuff. It's a great elk gun, though.
Half the fun of a new gun, for me, is shopping. I envy you the chance to browse the data and browse the gun racks, then buy something and shoot it for the first time.
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If God didn't want us to own guns, why did He make the 1911?