I'm a fan of the .30-cals, and used a .30-06 for everything for a while. Also done that with a 7mm Rem Mag for many years. I remember reading a lot of stories about the .270 Win as well with 130's for deer and antelope and 150's for moose and elk. That was a do-all big game cartridge. All three of those old timers are better than ever with newest powders and projectiles extracting the maximum performance.
Over .30-cal there are lots of good options as well. I'm a fan of .338-06, .35 Whelen, and 9.3x62 - they might suffer a little on trajectory for a long poke on a pronghorn but chasing moose in thick cover they are hammers. Obviously you could step up to .338 Win Mag, .358 Norma (or STA - might be my favorite!), or 9.3x64 but those generally exceed my recoil tolerance for a box off the bench.
8mm isn't spoken about much but my uncle had an old Mauser that had been reamed out to 8mm-06 that seemed like it would be a hammer as well, he always had issues finding ammo so I handloaded it for him for a while. I think 170gr Speer bullets? I can't even remember anymore, but wouldn't mind seeing that old rifle again.