In for answers. I have a .243, which appears to be nearly identical in size and ballistics to the 6mm Remington. For deer, I have chosen an inexpensive load that I can buy on sale pretty cheap at sporting goods stores or WalMart. It's the Hornady American whitetail, 100 grain soft point.
Muzzle velocity just a tad under 3000 f.p.s.
it shoots tight groups at 200 yards. I have not shot it any farther, yet.
I don't expect to see, or try to attempt, a shot over 300 yards anyway.