I would respectfully disagree with the gentleman about cartridge design not having an effect on accuracy.
50 years of use and development in benchrest competition has shown that a few cartridge design parameters are conducive to accuracy. The development of the 6 PPC, and it's dominance in benchrest competition is the prime example. When Mike Walker of Remington decided to try and unseat the 6 PPC as "the" benchrest cartridge, he basically came up with a bigger 6PPC, the 6BR. Short, realtively fat cartridges, with a long neck and shoulder angle that tends to keep most of the combustion turbulence in the case have been proven for almost 35 years to be dominant in benchrest competition, where pure accuracy is the only requirement.
In High Power across the course competition,(200,300 and 600), where ballistics, ( wind deflection), is almost as important as pure accuracy, the 308 is a strong contender, as is the 6XC, 6BR and the .223.
In High Power Long Range competition, ( 600-1000 yards), the ballistic abilities of the cartridge become even more important. At the long line, the 308, 6XC,.243, .243 AI and the 6.5-284 are popular.
In 300 Meter competition, the 6BR rules.
In 1000 benchrest, where rifle weight is of no concern, big over bore magnums rule, even though IIRC, the current world record for group size is held by a 6BR.
Over the last 20 years, National High Power championships have been won with several calibers---308, 243, 6.5-308, 7mm-08, 22-250 and 6mm Hagar.
Almost any caliber can shoot accurately with the right equipment and reloading skills, but for pure accuracy, read Precision Reloading or Benchrest.com and take tips from our Benchrest brethren. Most of us aren't concerend with a sub .200" group size, but if you are, the 6PPC is the current king of the hill, and has been for 30 years.