Yes the 308 is enough. I prob use a little heavier bullet then a 150grn like a 180 and prob use one with a little better construction then a corelok, with factory ammo I prob get a bonded bullet or a Winchest CT bullet which costs more then the coreloks but are usually more reliable.
The only issue you may have with the 308 is if you are shooting extremely long ranges like 400+ yards. You may wish you had a larger gun but anything in the 300ish yard range or less youll be fine. Just practice some longer shots if thats what youll bedoing.

30-06 would def be a waste of $ if you have a 308. If you want to go up to a Magnum or short mag in a larger caliber ie.. 300 or 7mm or 338 or something like that would be worth the $ but still wouldnt be NEEDED.

Good luck on trip.