1,000 yards is more about the bullet than the gun. You need a long low drag bullet to stay supersonic out to 1,000. That translates to barrel twist. 12" twist is marginal, 10" twist is just right for stabilizing the bullets with drag coefficients greater than .475.
If you want to make holes in paper and hunt, consider a 6.5mm cartridge. The 260 loaded with a long, low drag bullet is a great 1K yard round and won't break your shoulder or bank account. The 6.5X284 is a dominating 1K yard round. Heck, my next gun will be a .243 and with a fast twist barrel and long bullets that will be a great 1K yard performer.
I used to compete at 1K yards with my 30-06 hunting rifle (10" twist and 4-16X scope) and could beat about half the guys with their tacticool rigs. I didn't get teased much because they knew if I beat them I would rub their nose in my 21" skinny barreled wood stocked sporter.