On the other side of things...
My Tasco 3-9x32, that is older than me, attached to my 200$(Okay, back in 1969) Parker Hale 7mm Mag (Mauser 98 Sporterized), hit caribou at 200 and 300 yards in -35 degree temperatures. The close one I had to chase down, the further one dropped like a rock. The rifle has a Timney single set trigger.
The rifle now has a Burris Fullfield II 4.5-14x42 scope.
The Remington 700 SPS varmint is a nice gun for 500$. Throwing a nice 500$ scope like a Nikon Monarch or Burris Select would be a great addition. Then go get a trigger. 700 actions are arguable the most accurate for the price. But they are not the strongest. Weatherby, Winchester model 70, etc. make stronger actions. Ed Brown makes some tough stuff, but they are 2-3k.
Savage is slightly more accurate out of the box, but also more cheap in quality. It also has the funky trigger.
You can go out an get a 2-3k rifle (Sisk
) and a 2-3k scopes Kahles, Swarovski, Scmidt & Bender, etc.) and have it setup for you as well. But the deer aren't going to get any more dead.
High dollar Sako's break stocks as well.
Ruger has a target model as well. Ruger isn't known for being highly accurate. But they are strong and reliable.
Do you want a bench rest rifle, or hunting rifle?