Remington 700 LTR (light tactical rifle) The have a HS Precision stock, free floating, fluted barrel of 20". Great 800 yard rifle. Mine likes the 168gr SMK, absolutely loves the 168gr Amax, and shoots the 165gr Speer BTSP almost as well as the SMK. These loads are all u der .5 MOA at 100 yards with handloads I run. Factory SMK in 168gr, and the BVAC 168gr Amax also do extremely well. I have no lroblems consistently hitting softballs and spray paint cans at 500 yards.
If you are serious about 1000 yard shooting I recommend going with a longer barrel and 1:11 twist to stabilize the heavier bullets better (175gr & 178gr). The Remington. 700 LTR is brother to the 700P, and I think it's the best you can do for $900 - 1000k. I enjoyed shooting it more than the Sako TRG42 I used to have for the sole reason of barrel heat. The 300 mag heats up barrels fast, and the 308 does very well at sustained courses of fire. Just something you may want to consider when choosing your rifle.