257 wby,100 gr triple shoks.
This load will take down any Mule Deer that walks the planet at any range you can hit them in the chest.I use a 25-06 with 115 Barnes x,and have killed many mulies(as with Nosler,BT,seirra's and coventional bullets).
If you might cross a elk's path while deer hunting I would use the 7mm RM with 140 noslers,accubonds,or x's(the 257 weatherby will work also)

As for meat damage use a good bullet that will hold together.try not to shoot straight through the shoulder,the bone fragments shrapnel into the meat.
BBJ