For hunting in the the USA only, with accurate off the shelf factory ammo, and complimentary to your “eventual” inheritance, I suggest .270, 7mm08, .308 and 30-06 in that order. All are capable, easy to shoot well, and adequate for any game you will hunt at reasonable “traditional” range. More is not always better. It’s easier to learn again how to shoot accurately from field positions with a cartridge that doesn’t beat you up with recoil. I love the 7x57 and have three of them, but it’s not a practical choice for your stated goals. The .280 and 7x64 are also wonderful but too unusual in the marketplace for your stated goals. The 6.5 Creedmore offers a little less power than I’d be fully comfortable with for moose or elk. A hand loaded 6.5 Swede would be OK, but you said you need good factory ammo which is scarce in the USA for that caliber. Same problem already stated for the 7x57. Any belted magnum is not necessary, and will overlap with your future .300 & .375
So my suggestion is go rifle shopping. If you find one that you really like in .270, 7mm08, .308, or 30-06 buy it with confidence. The rifle matters more than the differences between those cartridges if it fits you, functions perfectly, shoots accurately, pleases your hand, eye and wallet.