I think you need to look at where you'll be hunting, what you'll be hunting and the distances you'll be shooting as well as the availability and expense of ammo. If I were to only have two hunting rifles in my cache, I would choose a .22lr for squirrel, rabbit, groundhogs, raccoon, etc. (Yeah, you can eat 'em all, as well as possum, muskrat and a few others). For larger game, I would choose a pre-2009 Marlin 336 30/30. Pre 2009 because that's when Remington bought Marlin and it became a Marlington - less attention to the QC. Marlin because it's side eject and will accept a scope a lot easier than the Winchester 94. It will take any game in North America including bear (although I'd hesitate to hunt Griz with it). Scope on a 30/30? Well with advent of the Hornady LeveRevolution ammo, the effective distances have become such that a scope is now practical on a 30/30 carbine.
The 17 is a great round, and the effective distance is much greater than a .22lr, but how often will you be shooting squirrel at 200 yards or more? Same with the 5.56. And the 5.56 round is a little small to be hunting big game (in my opinion). .338 Lapua costs you a buck and a half every time you squeeze the trigger. You can do better with a 30cal type gun - 30/30 for example.
Just my opinion based upon my experience, ownership and shooting. As with all shooters, the more I learn the more I realize I need to learn. So, the foregoing is not anything other than opinion.