I love the 308 round, its my favorite, but I dont really look at mine as a 1k gun. More like a 800 yard gun max. And not get into serious wind and drop issues. Savage actions are the way to go in my opinion. Model 10-12 are great. Even the older long actions will be great on a new build. But those are hard to find and stocks are rare. You can swap out barrels/calibers in 10-15 minutes without the need of a smith with savage. Get a savage. That being said, Id go for a 18-22 inch, 10 or 11 twist barrel. Those lengths are ideal for carrying. Anyhing longer and it just gets in the way. As mentioned, the viper vortex scopes are great for the money. Scopes rings, I use Weaver low 30mm 4 holes. They are rock solid and a great buy. Quite a few choices for bases. Talley, EGW (aluminum), Weaver, Nightforce (expensive) and Badger (expensive). Some others. All make solid 20 moa bases that will get you to 1k. Lapua brass and a good bullet. Sierra or Lapua. Powders, Varget, imr 4064, 4895 or 3031 will get you where you need to be. Dont think you have to have a $3500+ rig in order to shoot accurate at 1k. Ive seen rigs a lot more expensive shoot worse than my "cheap" $1700 setup. Key is, practice practice practice. Shoot shoot and shoot some more. Ive almost shot out a 308 barrel I got 3 months ago. Practice.
Oh yeah, invest in a chronograph if you dont already own one. Its a must. Good luck.