If you bought the rifle, well it is just a quality scope and mounting system you need. I would go further the the Nikon. Repeatability is very important in shooting distance. Up 10 clicks, down 10 clicks and scope returns to original zero. Less expensive scopes do not do that well. This is a better option for that magnification range.
I agree you need good optics and finding what works best in the rifle such as hand loading. My cousin is big into makeing his rifles shoot straight and true. Put three nails in the the target at a 100 yards and drive all three all day long. Hand loading good optics very important
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I have the Savage 111 in 30-06. Mine has the accutrigger but not the accustock. As far as accuracy it stands at the top in my collection. I was surprised to see the accuracy it gets right out the box with a sporter barrel. After a good bit of trigger time behind this rifle, at 400 yards with a pumpkin size target I'd make that shot 9/10 times. I have a 3-9x40 Nikon Buckmasters with BDC reticle. Good combo. I have had great luck with Hornady 165gt Superformance ammo. Not the cheapest for target( it's my hunting load), but that is the factory ammo that has been most accurate out of my rifle. The rifle itself should be more than capable for you. As others stated it's the scope that will limit you.
I bought my savage 111 (.300 Win Mag) back in October, and recently purchased a Leupold VX-3 for somewhere around $450-$500, and it has preformed flawlessly. I really want to test it out at 600 yards, but so far 200-300 yards is a breeze. But the scope has played a major part in accuracy.