The two best points so far have been to invest in your glassing skills, and your shooting speed.
Having done a fair share of mule deer hunting in open country, I would also recommend taking the time to learn where and when to look. Big Muley's act totally different than medium sized mule deer. In addition, figure out before hand what you want to shoot. If it is going to be a nice 28" buck, you have to be willing to pass on a 24"er.
As far as rifles go, a .30-06 shooting 180 gr. Hornady BTSP will kill a big buck at 600 yards, no problem. If you want something new to you, I would stick with either the .270, .280, or .30-06 in a AI configuration. Plenty of power that is still manageable in a light rifle.
