You need to go over to SnipersHide and SnipersParadise and lurk for a while, reading the archives. You'll learn a lot.
For long range shooting, you want an accurate rifle, good optics with the rifle features, high BC (ballistic coefficient) bullets, and high muzzle velocities.
Suggested calibers include 50BMG, 338LM, 7RM, 6.5-284, 260REM, 300WM, and even 308.
The 190gr SMK, the standard 300WM loading, has a lower BC than the 160gr 7mm's and the 140gr 6.5's, so it'll have a little more wind deflection at 700-1000 yards (a few inches). Of those, barrel life will be longest with 308 and 260REM.
It's certainly possible for someone who knows what's he doing to build a Remington 700-based rifle for about $1200-1500 and have it be accurate. If you're lucky, a stock 700 PSS or Sendero might, but you might also get one that doesn't shoot.
On the other hand, you can buy a custom gun from an outfit like GA Precision (GAP), HD Rifles, Robar, etc.
Or you can buy a "factory" gun in the class of the Sako TRG-42, Accuracy International, etc.
I suggest looking at the Leupold Mark 4 M1 scopes as the "baseline" and moving up from there if you can afford it.
-z
ETA:
By the way, here's a spreadsheet giving drop and wind deflection numbers at 800 yards:
http://www.demigod.org/~zak/tmp/ballistics.html
Sorted best to worst by wind.