Another great all-around hunting caliber that hits the sweet spot in terms of ballistics, availability, and recoil is the .270 Winchester. The cartridge for the .270 is longer than the .30-06 and a bit faster. The bullet is a bit smaller.
There are lightweight rounds available for varmint hunting (it’s a tad on the large end for that), and 150-grain bullets available for hunting larger game like elk, moose, caribou, etc. That is to say it’s close to as versatile as the .30-06.
Muzzle velocity for a 130-gr bullet is around 3,100 fps and it can travel quite far. If you’re hunting in mountainous terrain and expect to make long shots a regular habit, the .270 is an excellent choice.