I went to Kyrgyzstan a few years ago and used a .300 WSM
w/ a 150 gr TTSX. I get real nice 1/2 in. groups with that load. My Ibex was 400 yards. My son used his 7mm. His was over 500 yards. Be prepared for long range. Where are you going for your hunt?
The .308 will do fine. Just use a good bullet. Know what your shooting limits are. Good luck. Bruce