Since you are just punching paper, no need for the .308. I like the .308 fine; it's my preferred hunting round. And I have an accurized 700 VSSF in .308 with which I have shot steel out to 900 yards with 175 grain Federal match ammo.
But just to punch paper you don't need the terminal ballistics (or the recoil) of a .30 caliber round. I'd opt for the .260 Remington or 7mm08. They are based on the same case but have higher ballistic coefficients than the .308 when using heavy low drag bullets.
The one advantage of the .308 over the two aforementioned rounds is that it is more commonly available, and may be had more cheaply in bulk, as long as you're not buying match grade ammo. You can't go wrong with a good .308. But you can do better.
As far as rifle is concerned, Savages are considered to be among some of the best "bang for the buck," with outstanding out-of-the-box accuracy. Personally, I don't like the accutrigger, much preferring a well-tuned Remington factory trigger or one of the easily-installed replacements. I think the older Remington 700s have more "class" than the Savages, but beauty is in the eye of the beholder. Years ago I'd have said "Remington 700, no question" because of quality and the availability of replacement and custom parts. But Remington's quality seems to have slipped in recent years, and more and more aftermarket parts are becoming available for the Savages. You really ought to handle both and decide which one you like better.