If there was a single BEST, my safe would not be overloaded...
Most of my rifles have been at or below this price point. The following is purely my personal, subjective opinion. All of the following will shoot MOA groups with the right ammo if I do my part.
It gets down to what bells and whistles you want. For aesthetic appeal, I happen to like the external claw extractor and three position safety of the RUGER 77 family (I have three in different configurations). For pure out-of-the-box accuracy with about any ammo I have fed them, I like the Tikka T3 and T/C Icon/Venture. (BTW, for an interesting comparison, put a Tikka T3, T/C Icon, and Ruger American side-by-side. I am not sure if there is a generic name for this type of bolt action, but these look like brothers...).
For the record, I don't particularly like the Remington 7/700 series (I have 2). I have never been happy with the finish on the wood stock of a Remington rifle. Also, for the record, the most accurate rifle I own is a Model 7.
The Savage is a workhorse (a heavy barreled 22-250 old pre-accutrigger model used for varmint control).