I've been hunting elk with my .308 for 38 years and none have gotten away yet. Plan to fire two quick shots into the chest organs for fast kill. My farthest shot was approx 225 yards or so.
I like the performance of FEDERAL 180 grain Fusion ammo but have also had good luck with 150 grain Premium ammo by Winchester. Elk are not armor-plated at all but they don't always react to a good chest strike like smaller animals. So practise firing two quick but accurate shots to prepare for your hunt.
Fire up the grill! Deer hunting IS NOT catch and release.