I dare someone to name one animal in Indiana that won't drop, with proper placement a cci short CB. .22 SHORT,LONG AND LONG RIFLE GETS MY VOTE. Next would be a bolt action .243 it will roll out to 1000 yards with relative ease.
My vote/choice would be totally dependent upon the region of the country.
Here in the midwest there is no need for anything more than a 308 and other calibers might be far more flexible on smaller game yet still take down the largest animals we have here.
Go farther north and there are animals like Moose that would require a larger caliber. Go out west and there are both big dangerous animals that can eat YOU and there are animals that require long flat shooting calibers.
Here, in Indiana, I'd probably go with a 6.5 Grendel, perhaps a 243 Winchester, maybe a 260 Remington, and there is an outside chance of a 7mm-08. All are capable of dropping a deer for food, a black bear that might be a bit too aggressive, a coyote at 300 yards and yet each can be loaded with light bullets suitable for varmints and smaller game (with the possible exception of the 7mm-08). The reality is that a "single gun" is very likely to be used to harvest a lot more rabbits than deer, hogs or bears. Consequently a gun that is not TOO MUCH gun is going to be a more practical choice than an uber-magnum sledge hammer.
I have the REM. 700 IN .308 and .22/250 and they both shoot fantastic. It would be a hard choice, I guess it would come down to where I'm at, if in Ind. I can't think of a critter here that the .22/ 250 won't handle, if out west with the larger game my .308
If your limited to just one rifle, then either a .270 Winchester or 30.06, both have wide range of bullet sizes and ammo selection, commonly available. The 30.06 ammo is easy to find good deals on. My third choice would be a .243.
If you want a rifle to use for coyote as well as deer or larger, I think the .270 gets my vote for overall versatility, its a real flat shooter, very good ballistics. I use a .270 with 100 grain bullets for coyote. Some guys say its too much rifle for coyote, but if your limited to one rifle, I think its fine, and the fact that its such a flat shooter makes it good for long range.
I have a Remington 700 XCRII in .270 and a Remington 700 BDL Deluxe in .270 - both are tack drivers. I also have a Weatherby Mark V in 30.06, also a tack driver. 30.06 comes in so many different bullet weights and loads that you could use it for just about anything in North America from deer to elk. Same case could be made for the .270.
I voted for the 30-06 with my wallet back in '07 when I ordered my custom from Savage. I use mine at the range for shooting out to 1,000 yards using 168gr and 200gr matchkings and I've taken it bear hunting using 220gr gamekings.
The only problem with the 30-06 is that it's not new. It's not some cute little 6.something caliber gun that's ok for girls to shoot, and it's not some whopper magnum that all the guys with the insecurities need to feel like a big boy. If Hornady/Remington/Winchester released a "new" cartridge today that was advertised to have the versatility of 308 to 300 win mag and the accuracy or either then it'd be a big hit. Instead, it's just an old reliable caliber that doesn't get the glitz and glamor of the gun magazine, but somehow you'll always be able to find ammo for it on the shelf of every mom and pops gas station/general store out in the middle of no where.