1000 yard gun: 6mm, 6.5mm or 7mm. Any of them can be built on a Savage, Remington, or AI rifle that will do better than most can shoot. AI stock. Harris swivel bipod. 20 or 30 MOA scope base. Something AT LEAST 16x in the scope.
500 yard hunting rifle: What are you hunting? Varmints - those rigs are a special breed by themselves. Big game (deer and up) - Tough to justify shooting further than 500. Tough to justify shooting on non-bedded game past 400, honestly. Animals move. Bullets aren't lasers: they are affected by wind at that distance, and they shoot at an arc. If a deer takes a step forward while your bullet is in flight, it changes a clean chest shot to something messier - if you got your range estimated right in the first place. Shooting past your MPBR requires a range finder, in my humble estimation, because otherwise, you're just guessing, and ... there's too many variables for that.
All that said, you want a very accurate rifle for shooting past 200 yards. Up to 200 yards, you can do fine with up to a 4MOA rifle. Past that, you want something more precise. Many manufacturers make very accurate rifles in calibers that will carry enough velocity to kill past 400 yards. If I'm in a humid environment, I want a stainless barrel and action. If not, I'm fine with a blued barrel and action. Synthetic stock - I don't like warping, and I don't like worrying about scratching up pretty wood. 2x7, 3x9, 4x12 scope. I don't want weight, and I don't want anything too terribly expensive. If I slide down a hill on my rifle again, I don't want to be cussing because I just damaged/destroyed something I can't afford to replace.
My current rifle is my perfect rifle for hunting. It will probably wear nicer glass and a better scope in the next couple of years, but neither will be dramatic increases. I have a Savage 11 with a detachable box magazine. Everything you need to put deer down, nothing you don't. I personally won't take a shot on a deer past 400 yards at present, because that's as far as I know I can make a hit, and I want to be closer than 300. Closer is better. For having fun shooting long distances, I'll go back to the range and punch steel. For deer, I want to be closer.