I can shoot an inch or a little better at 100 yards with my factory 15 incher shooting 150 grain BSTs or SSTs over IMR 4064. Your accurate range depends on your proficiency with a handgun, but the .308 is a 250-300 yard cartridge out of a 15" barrel. I wouldn't try a 300 yard shot with mine, but that's my personal choice, not a failing of the cartridge.
I heartily recommend a .308 handgun, but like the others, advise against the muzzle break. With a little practice, you should be able to tame the modest recoil of the .308. Have fun!