Wow, zombie thread! To the main point, a thousand yards seems a little unrealistic. At that range, I think accuracy depends a lot more on the shooter than on the rifle itself. I'd certainly not go lighter than a .308, and even then I don't know how well it would do at that range. Not that I'm an expert by any means, but at that range you'd probably be better off with a .338 Lapua Magnum or a .50 BMG.
.
By the way, what on earth do you want to shoot at such a range, anyway??!!