Seems to me that most of today's rifles will shoot pretty good, right out of the box. Further, it takes little work to do some tuning, to tighten up the groups. (Mostly, just a little tweaking with the bedding.)
IMO, there is no way that any factory can mass-produce rifles such that ALL are splendiferous. Based on comments here at TFL over the last three years, I'd say that the Remington 700 seems to have the edge--at least in your price. Note that quite a few folks who post here have had equal luck with many other brands, as have I.
All in all, I tend to believe that fit and feel, coupled with your own sense of aesthetics, should be more of a determinant than brand name. If hunting is your prime consideration, a rifle which fits properly and feels good when you quickly mount it to your shoulder is the one with which you will shoot the best.
Best luck,
Art