For the 600 yards get a factory rifle in 338 winchester. Does great without a brake. I prefer the tikka t-3 light in 338 winchester. 600 yards does not require the extra cost, noise or powder consumption of anything bigger than the winchester.
Now for the mile. Get a nice custom rifle
designed for that when you are ready for it. The 338 winchester shooting the 225 grain Rocky Mountain bullet with a .773 BC at 2950 fps will get you the mile. But a mile needs a good custom rifle