Get the Savage, unless you feel like spending 3x more for one of the stainless Winchesters.
I generally like Ruger but their bolt-action rifles don't get good reviews for accuracy or triggers.
I owned a Remington 700, and while there was nothing wrong with it, nothing really impressed me about it. The trigger was too stiff, the stock (polymer) was too flexible, and it just felt like a price-point consumer gun. The Savage does to some extent also, but it costs less and will likely be more accurate.
I've since gone to an FN PBR (almost the same as a Winchester model 70) and it's just a much nicer gun in almost every way.
The other reasonably priced rifle I would look at is the Howa 1500. Quality, cost and accuracy will all compare well to the Savage or Remington. But it's harder to find and made in Japan vs. the USA, so there isn't necessarily much reason to prefer it over the Savage.