Do you reload? If not, do you plan on reloading? I think your answers to these questions will help guide your choice. Where are you and what are going to hunt? I've read lots of posts from people convinced they need a 300 RUM but live in areas where the furthest they can shoot is 300 yards and they are only after whitetails.
If you reload, then the options open up considerably. You can make the ammo for whatever caliber you choose. For 1,000 yards, the .308 is not the best choice. While it can accurately hit targets at 1,000 yards, there are other calibers that will hit the same target with less drop and more energy.
If you don't reload, I would look at the more common calibers. A 6.5x284 round is an excellent choice at 1,000 yards, but at least in the southeastern US, it is an extremely difficult round to find on the shelves. Same for .260, 6.5 CM, and any of the AI calibers. You can find .30-06, 7mm, 300wm at any Wal-Mart, sporting goods store, or country store that sells ammo. All three are very capable of 1,000 hits.
If you ever travel with your gun, it would help to have a common caliber you get ammo for anywhere as opposed to one you have to get online.