I got a nice 30-06 with a very nice scope for $275 used at a gun store. It’s a dang canon.
I got a brand new Savage Model 110 in .308 with a factory set Nikon BDC scope out the door at Cabelas for less than $400. Its by far the most accurate rifle in my possession. It also has a superb adjustable trigger.
At 100 yards I can cover a 3 shot group with a quarter.
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It's probably Pachelbel's ...
Any used Remington 700. The old man probably hadnt fired more than 3 or 4 boxes of ammo through it his entire life. Then the widow hocked it. There are lots of these around that have probably been fired less than 200 times. I got one with a scope for about $350 and paid too much for it. It shot touching holes with one load I worked up. Then I found a Remington pump in .270. I had one load that did better than touching holes. I think I paid $400 for it and it was a steal.
A lever action 30/30 would be more than enough gun for deer hunting in the lower 48 states. A used Winchester or Marlin can usually be found in the $200 range at most pawn shops, just check them out well before the buy. Look for older Marlins.
If you are hellbent on a bolt action rifle Savage would probably be your best bang for the buck and the caliber, .243 or bigger.
I passed many times on a US M1917 Enfield 30’06 caliber rifle that had been drilled and tapped and already had a good scope on it at the local pawn shop a few years back. $210OTD was the price. After 6 months of it sitting I came in to buy it and offer $200 and it had been sold right as deer season started.