is the 1000 bones for the entire set up or just the rifle? if just the rifle, I'd look at the Howa's, or Tikka T3's. If that money is for gun, scope, bipod, sling, etc. I'd still get a T3 and what ever is leftover would be spent on the scope.
if you really want to spend 1000 or close to it, a Kimber would be my first option. But I feel as if I can get the same quality from a Howa, or Tikka/Sako rifle and save a few bones. I just know my scopes are in the 600-800 range so any savings I get from a rifle goes to the glass/stuff. All the rifles listed will shoot sub MOA if you do your part. I know I cant shoot better then my rifle so I accept the .75-1 MOA I get.
TimeOnTarget has a good suggestion. I own this rifle and it's my go to gun it holds up to the nasty weather in Alaska and everywhere else Iv taken it its accurate and light and shoots really nice. I put a vortex viper on mine
Get the Tikka and put the rest toward quality glass. I love my Tikka .30/06 with Zeiss Conquest. I'm not much over your $1000 budget with rifle AND glass. Pick up a recoil pad too because it will thump a little bit.
Before I would recommend something I would need more info. What kind of shooting are you going to be doing and where (ie mountain hunting vs stand hunting)? Are you looking to customize or off the shelf? Do you want a detachable mag or internal? Are you wanting to push the limits of that 30-06 or are you keeping your shots closer? There is always a trade off as the lighter you go (Tikka T3 for example) the harder they are to hold steady and the more punishing they are. The heavier you go, the harder to carry around but easier to stay on target. So far all of the rifles mentioned are really good. I too am picking up a new one and going with a Savage for a variety of reasons including, out of the box accuracy, trigger, ability to swap out barrel without needing a gunsmith. I have shot many different rifles and the one I am getting also fits me well. There are so many great options out there, it just depends on what you want to do with it beyond just shooting. I have owned Remingtons, Winchesters, Brownings, Sakos, Anschutz (wished I still had those) Rugers and I am sure I am forgetting a few. My family has owned a small gun shop so I have had access to a bunch! The Savage I am getting is the Bear Hunter in 300 win mag as I love the feel, the accuracy and the adjustable on/off muzzle brake. It is also light enough to handle pack in mountain hunts be very capable at 1000 yards as well. I also looked very hard at the Tikka as well. All the guns mentioned are better than most shooters, you just have to figure out what you are mainly going to do with it and go from there.