Im going to recommend a Ruger. Four your price you can get the Ruger and a Burris Ballistic Plex scope.
Every Ruger I have is a great shooter. Except for my VT which is unmodified, I havent done any more to them than I do to any rifle float the barrel and touch up the trigger. My hunting buddys Ruger is also an excellent shooter, as are my brothers.
The Rugers have the best scope mounting system available IMHO, and the rings come with the rifle. Solid one-piece bolt, three position safety, controlled round feed, great looking but rugged and reliable. The Ruger stocks, although very good looking to my eyes, do not have the fancy white line spacers, fore end cap and high-gloss finish that some other rifles have.
As to accuracy, all my Rugers shoot MOA or better with the right loads. I handload for the most part but generally keep a box of factory stuff around for my big game rifles. Accuracy with the factory loads has been outstanding as well.
Dont overlook used rifles, though. I just picked up a very gently used 1975 Remington BDL in .308 Win on the cheap for Christmas. I floated the barrel and took it to the range to adjust the iron sights before scoping it. Its another shooter.