7mm and 0.270 are substandard at long range for competition shooting, make sure whatever chambering you choose has a good selection of bullets available for it, you are going to want to hand load your ammunition for this task. At long ranges the 6mmBR is still the best all around cartridge out there. For more information on long range shooting go to
http://www.benchrest.com/ and you will find most of the information you could need in the forums. And be warned to be competitive get ready to spend a lot of money on a rifle based on either a heavily modified sleeved Remington 700 short action or one of the various custom actions such as Farley, Stiller, BAT machine, RPA, etc.