There are many here that can help you way more than I can as I have only shot one elk and it was not with a 308 but at the time I was considering using my 308 so I did do a lot of looking at bullet possibilities. First, do you reload? If so, you will have way more possibilities. I do not, so I am somewhat limited. I would go with a 165 or 180 grain high BC bullet such as a Nosler Accubond, Barnes TTSX, Federal Trophy Bonded Tip, or Federal Copper. I was going to use the Nosler Trophy 165 gr accubond due to ballistics and that is what my rifle shot the best. I was getting 5/8 inch MOA and was going to be hunting above 10,000 feet so the numbers were pretty good. Federal makes two different 165 gr Trophy Bonded Tip rounds. One is high energy with a BC of .450 and a MV of 2880 but the only problem was I could not find any. I called Federal and it is a special run which they only do once a year in limited quantities. If you can find it, good luck, it is Vital Shok P308TT4. I suggest looking at some of these and choose what looks good then plug the data into the ballistic program here at the elevation you hunt and see what produces the most energy. Then you will have to get one box at a time to see which one gives you the best accuracy. Not reloading, I had to go through 5 different brands until I achieved the accuracy I was looking for.