You're in Arkansas- is there an Academy store near you? They list the Mossberg 100 ATR (with 3x9 scope mounted!)in several calibers for $300, & according to the weekend ad that's a regular price. Repeat, rifle with scope mounted for $300. If you handle one & think it seems OK that's probably gonna be the low-buck champ, Comes in .30/06, .308, .270, & I think also .243.
Academy also offers the Savage Axis in several suitable chamberings for $280- but that's a bare rifle, no scope or even iron sights.
If you can find something used you may get a nicer rifle for a good price. As a near-lifelong Winchester Model 70 owner(pre-'64 Featherweight, .270 Win), I say if you find a decent deal on a used M70, Jump On It!
But: If I was gonna buy new & was on a tight budget where every $ counted(sounds like that's your situation) I'd get to an Academy & at least look at that Mossberg 100 ATR rifle/scope combo. Then, if nothing else, you'd know you didn;t like it.
Some other lower priced models you might want to investigate: The Stevens 200, & the Marlin XL7. if you're willing to consider a break-action single shot, Academy has those for ~$200 in several good deer calibers. But you'd need to add scope & mounts.