I'll be different. Not surprisingly, a lot of people are saying 308. You've even got a couple 30-06 and at least one 30-30 in the mix. I'm going to assume you already have a bolt action 22 LR. If you don't I'm going to suggest you get one of those first. Doesn't have to be a top shelf gun--just get a Marlin. It's a hell of a lot cheaper than anything else you'd get in center fire cartridges, and even with ammo shortage, cheaper to feed when you can find a brick. Bolt action does not waste ammo and is accurate. Take the rest of the money you'd have spent and get a couple bricks. It's the last rifle they'll confiscate, has the same recoil as a bb gun, but will go through a 2x4 edgeways. Yes, a properly placed shot from one with 25 - 100 yards will kill nearly anything. In time of war (WROL), economic hardship (you might have to hunt out of season), etc, it's one of the most quiet. Meaning getting meat is easier. As for money spent practicing for basic accuracy, you still can't beat it.
If you've already got one of those, my next pick is a pump action 12 or 20 guage with screw in chokes and replaceable barrels. The gun will literally hunt everything with a long barrel. Get one with shotgun barrel and a slug barrel, then you have an instant 50 caliber or larger rifle for big stuff within 100 yards or so and a small game gun. My pick: Rem. 870.
If that's covered too, only then I suggest a bolt action 308 or 30-06. I like the 308 for less felt recoil. I like the 30-06 because you have 110 years of reloading data to draw from, and a wider range of reloading options. Ammo for both is plentiful enough for now, but learn to reload. As for the brand--your wallet is your limit. Savage is an accurate rifle. Remington 700 is too and can be customized as much as you can afford. Both can be made into long range match rifles, but a guy who does it regularly tells me he likes the Rem 700. I used to love my old Ruger M77, but their quality tanked--at least that's the impression I get holding one. Now I have a Browning.