For that price, a Savage would be a great choice...and I'd suggest in 243; there are loads for smaller varmints and for deer-sized animals; accurate out to the range you want, flat-shooting, and less recoil by far than the 270.
But, like others, I'd suggest a 22LR first; Ruger 10/22 or S&W MP 15-22; either will be addicting and lead to a life long collection of guns.
And please don't think you can stand up to a charging Grizzly with a bolt gun.
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