I get 1/4 MOA groups with my factory Savage 111 FCXP3 in 300 Win Mag shooting handloads. It shot 1/2 MOA on the first batch of rounds I loaded for it, and using the little 3-9x Bushnell scope it came with from the factory. After some load development and adding a 6-18x Nikon Buckmasters scope, I shoot consistent 1/2" groups at 200yds. I have what you described and I only paid $700 for it ($400 for the rifle, $300 for the scope). I might have just been one of the lucky ones, but my vote is get a Savage and use the money you save to put a decent piece of glass on it.
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