Re: Best caliber/rifle for 600-1000 yards.
270 got all the praise from gun writers for very good reasons. But there are other fine rifles for what you do. You might want to look at the 260 Remington, 7mm-08 or other cartridges where bullet BC can give you a much better performance margin than the 30-06.
Please don't misunderstand me, as I think the 30-06 is one of the finest all round cartridges of all time when the right twist rate is used. A 1-10 twist will allow you to use the very heavy 30 caliber bullets, but recoil gets to be problematic over the long run. That is why many shooters are going to cartridges in the 6.5mm (.264), and 7mm diameter.
There are really good choices in the 6mm class, but they tend to be a little harder on barrels.