Check into Browning and Tikka. For the amount you mentioned, Browning might be out of reach, but the Tikka's are a little less expensive and seem to be highly regarded. In general, Savages are reputed to have a good accuracy, out of the box.

I have noticed, in more than a few posts, that people talk about changing the trigger or bedding in their new Savage/Remington/Winchester. I don't think that you absolutely need to do those things, but I don't recall seeing comments like that regarding the Browning or Tikka rifles.