Easy answer, which, fortunately(?) or unfortunately(?), is always the answer: .308 Win (or 7mm-08).
But, more in line with my own preferences and opinion:
Whitetail, with the stated limitations?... .30-30, or maybe even a .223.
Add in other game in the lower 48... I'd be reaching for the .270 Win.
There are plenty of good cartridges in that list. My own experience and preferences have me in the 6.5 Creed to .30-06 range for the 'all around' cartridge. But, I'm a .270 guy. My poor '06 rarely gets any attention (although I have killed more animals with it than the .270 ...
); and I'd rather go more 'classic' with 7x57mm* than run a .280 Rem (or .280 AI, or .28 Nosler).
That being said...
If I really was having to decide on 'one cartridge to rule them all', I might finally consider diving into 6.5mm -- .260 Rem*, specifically. Why .260 Rem, and not 6.5 Creed? ...To be different*. And to stay away from the manbun bandwagon.
*Yea, I'm that guy that always has to explain what I'm shooting, after people ask. It may not even be a rare cartridge - just uncommon or non-mainstream - so most people just a confused look on their face. I prefer the uncommon: .307 Win, .17-223, .327 Federal, .275 Rigby, 6x45mm, .220 Swift, 6mm Pedophile, .475 Tremor, .444 Marlin (before the mid-west states change some rules and made that more popular), etc... Heck, I've even had people give me a dumb look after ".480 Ruger" came out of my mouth as the response to their inquiry.