Savage 10FCP-SR Long Range Rifle
The Savage 10FCP-SR rifle is probably your best buy for a 1000 yard rifle for under $1000. It comes in .308 with either a 20″ or 24″ fluted barrel, threaded muzzle, detachable 10 round magazine, over-sized bolt knob, and 20 MOA scope mount for around $650! Right out of the box, with factory ammo, this rifle has been shown to produce 1/4 to 1/2 MOA accuracy!
Simply add a scope and rings and you’re set up! Savage makes the most accurate factory rifles of anything on the market. In fact, Savage factory rifles are winning 1000 yard matches right out of the box, with no modifications or after market accessories or gunsmithing. If you want a rifle that you can immediately get out to the range with and start ringing steel out to a 1000 yards, this Savage 10FCP-SR should be at the top of your list.
About the only thing you may want to add would be a different stock or chassis system. A number of after market stocks and chassis are available for the Savage so you can customize it as much as you like.