No one mentions Remington? I have to throw that name in the hat. You can build a rifle on a rem action for around 1500$ keep in mind most competition rifles are built around or designs based off of the rem 700. I guess the savage accuwedge on a rem 700 equals magic.
Like packer, ikic, bb said. Optics is a must and to remphasize what packed 58 said, you can turn an average shooting rifle into an accurate one by investing in reloading. That is what is going to make your rifle shoot well. Investing time and more time into load development. One of these days I need to take a picture of my reloading bench.