Didn't read all these response so pardon me if this has been mentioned - 7mm-08 shooting 139 LRX or 140 Partition or 140 NAB. Or about any other "premium" 140 gr bullet. The 6.5 Creed/127 is another good thunk. If you really dislike recoil I'd also keep rifle weight ~ 8 lbs. I would not do a brake - but that's just me.
