Again, the easiest to get is a Savage 12FV in 223, a bit of bedding, handloads and you can play to your heart's delight out way beyond 1000m. Change to a limbsaver or hogue recoil pad, ballast lead front and rear of the stock so that your OA weight is around 15 to 18lbs.
That should make recoil very comfy and slow. Muzzle brakes would also work but can intimidate new shooters due to noise and concussion.
75gr Amax over Benchmark or varget, CCI BR2, Win brass, Lee collet neck sizer/seater should net you 1/2 MOA.
If you are sure that comp is in the near future, then you might want to go with a standard 308 bolt face and build a 6BR. All depends on your distance and rules.
If F class is what you want to play in, click on the link in my sig to see my F class 6.5 Mystic rifle based on a Stevens. Dirt cheap, moderate recoil, deadly accurate.
With the Savage/Stevens, you can mix and match parts to suit you needs.
Jerry