That's THREE.. LMAOIf it's only one cartridge, I would want it to be as versatile as possible. That would mean the heaviest game I might hunt down to smallest. So I would start with the biggest game I hunt and find the lightest adequate cartridge for that game.
For me that would be:
25-06 AI or similar with 131gr bullets for game up to deer. This would be great for targets down to varmints too.
264 Win Mag or similar with 150 or 156gr for game up to elk. This would still work for lighter work too and be comfortable to shoot often.
300 Win Mag + with 200gr+ bullets if big bears or moose were a consideration.