If you want to turn a .223 into a long-range gun, you need a barrel with a fast enough twist rate to stabilize the heavy match bullets that will fly relatively straight in wind and carry enough energy to keep going downrange.
You can find lots of bolt guns with 1/9 twists, which will probably work with at least ONE 75 grain bullet (Hornady's). But if you want heavier or more selection, you need a 1/8 twist or faster. After deliberation and counsel including in this thread,
http://thehighroad.org/showthread.php?t=225769
I just bought a Tikka .223 Varmint, in part because it has that 1/8 twist. The only other .223's I know that have it are AR's, which I just don't like. I've tried. Can't wait for my Tikka!
I chose 223 for specific reasons; but if you are unfettered by any competitive rules, or don't have bursitis in your shoulder, there are plenty of calibers that will get you out there easier. .308 is popular, of course--probably more popular than it deserves, since the main reason for its dominance is its police and military use. I mean, good round, sure; but it's got nothing on some more esoteric long-range rounds like the 6.5x.284. Even the 6.5x55 has lots of long-range fans, and not a few trophies to its name. 25-06, 7mm-08, .243 Win--lots of them will do. If you want to hit hard out there, .300 Winmag is a popular way to go. Not for me, though--no fun getting hit that hard!
So you want an accurate gun, probly with a free-floated heavy barrel, and either a good synthetic or laminate stock, for stiffness and stability. You want a caliber offering a selection of bullets with high Ballistic Coefficients, i.e., super-streamlined boattails. You want to read a bunch about wind and trajectories, and you probly want a piece of ballistics software if you don't already have one. Then all you need is a target 600 yards away, and a way to get down there and see where you're hitting!