Any rifle chambered in anything >/= .223 will get you out to 1,000 yards.
You have to decide though, what you would call acceptable. Is 2 moa good enough (roughly 20 inches at a grand)? Or do you need 1.5, 1, 3/4, etc?
If you think 2 would be enough, then most stock R700s or Savage 10/110 will...