If you buy either a complete standard mil surplus rifle (1903 or 1917) its going to shoot just fine.
Yes you can get cheaper ones, but the enjoyment factor in shooting an old mil surplus gun is priceless.
Or you can buy a well done mil surplus (you don't have to do it yourself). There are lots of them out there and beautifully done.
In other words you don't have to buy a project.
The only issue is price as a good mil surplus OEM gun runs 600 to 800.
Whats not said is your new Savage Axis will loose value and you will not sell it for more. A good OEM Mil surplus gun will gain in value in time and be worthy of handing off to the kids or selling for a good return at some point in the future.
Your Ruger All American will solicit no interest at the gun range, take a Model of 1917 Eddystone down to the range and you will meet and converse with the most interesting people and add massively to the enjoyment.