There is an often overlooked consideration in 7mms: throat length, twist rate, available ammunition.
I've found that the "European" and "Metric" 7mm cartridges have the heavy-for-caliber offerings, thick jacketed bullets, and have loaded ammunition suitable for elk, moose, bear, African game, etc. Not so with many of the "American" 7mm offerings.
For examples: 7x57 aka 7mm Mauser aka 275 Rigby has a "default" bullet size of 156gr to 175gr. Compare to the 7mm-08 that should be identical, but most of the ammo is in the 120gr and 140gr loadings. The throats in the 7-08 were not designed for the 175gr-180gr bullets (and by extension, the 140gr-150gr copper bullet that has the same volume as the lead 180gr). They shoot smaller bullets better. Thus, I avoid 7-08s.
Same for 7x57r, 7x64 Brennecke, 7x65r.
If you want to go the "American" route, a .280 Remington Ackley Improved is a solid choice. You can get factory loads. You can get heavy for caliber factory loads. You can shoot .280 rem ammo as well. It has the ability to take formidable game.