This is a loaded question
Seems all you will get from this question is opinions that will vary from gun to gun and from now on.
700 series - Remington makes a fine gun, the quality of late has declined (in my opinion) and the trigger will need work before it can fully reach it's potiential. All in all a great gun that will require some tweeking.
My 700's are fine guns and I can recommend as a good reliable bolt action with many after market mod's available. The 700 shoots about .5 MOA (for me) and fit and finish is great.
Winchester - Do not own one, have shot them quite often. I put Win just below the Rem in quality and reliability. Trigger is about the same, maybe a little worse, quality (I hear) may be an issue as of late.
Savage - Long action - I own two Savages I find the action is not as smooth as the Remington, but adequate for all my needs. The trigger (Accutrigger) is absolutely great, breaks at 2.5 pounds with no creep and breaks like glass. The double lug action is strong and safe. The barrels are of good quality but somewhat rough internally, this will go away after about 150 rounds. The group size is average .5 MOA at 100 yards for me, and I'm not a great shooter. The Savage sythetic stocks are throw -a -way stocks but the steel is second to none.
There are others to consider - Howa, Weatherby, and many others I have not mentioned and do not have experience with so I do not feel comfortable commenting on these.
From My experience I would recommend the Savage, with a decent quality aftermarket stock. I have not seen an "out of the box" rifle that will shoot any better than the Savage. I am speaking of rifles in the $500 - 1,000 range and I fully understand that the higher priced precision rifles will preform quite well. But any better than .5 to .3 moa with the Savage or Rem, is just minimal accuracy for dollars spent. If you into precision target compitition, look higher, if your into .5 moa accuaracy along with hunting go with the Rem or Savage,
Just my opinion
Dogg