Fore the most part (not always), its not the caliber that shoots the most accurate, but the gun. A weatherby is not usually a inheriently accurate round. It has alot of freebore. Roy, never intended it to be a benchrest caliber but a hunting round.

A 308Win and 223 are the standard "sniper rounds. And are available in most "tactical guns. I have alot of experience with the FN USA and can tell you, thier typical .5MOA is right on the money in a 308win. Its not the speed you need but shot repeatability. Short actions are usually the easiest. My 308 reloads get velocity spreads around 15fps. I am very happy with this. Then you use your scope for adjustment with target turrets. You have alot of reading to do. This FN has a chrome lined barrel, and doesn't copper foul at all. I mean at all.

http://www.fnhusa.com/contents/r_spr_a1.htm

I also have a 700P tactical. You can view them at www.remingtonle.com

They usually need alot of work to make them a full tactical rifle. I basically rebuilt mine. New barrel and all. Again, I suggest a 308.