Congratulations on the draw. You are in for an exciting hunt. It can certainly be a rush.
A 165 or 168 grain bullet (BT or AB) will work just fine for sheep. I recently developed some loads with bullets supplied by a gentleman. 168 grain Sierras with F210M primers and RL15 (charges ranging from 40.5 grains to 43.5 grains) all produced sub-MOA groups. Though this is a match bullet, using the 165 grain GK would likely produce adequate groups. 168 grain Hornady bullets with F210M primers and Varget (42.0 grains to 44.0 grains) all produced sub-MOA groups. Nosler 168 grain Competition bullets, F210M primers and BL-C(2) (40.5 grains to 43.5 grains) all produced groups less than 0.5 inches. I produced a 0.17 inch group with 168 grain Hornady bullets, F210M primers and 41.8 grains of IMR8208XBR powder. Choosing a good bullet (Ballistic Tip or AccuBond) and starting at the minimum load before working up slowly will likely permit you to develop a good load for your rifle.
Congratulations on pulling a Big Horn sheep tag!
I agree with Dr Mike's recommendations. I would add the 168 gr BT, it has a BC of .490 and would really make your 308 Win shine.
That is kinda what I am looking at for an all around load for my wife's 308 also. I think the 165 is about optimum for the 308. You can get good speed and with a BT or AccuBond you will have great long range characteristics. Scotty
Go with the AccuBond. It is the best of both worlds. Flies like the ballistic tip and starts to open up like it but holds together like the Partition and keeps on trucking. Varget , RL15, IMR 4895 for powders.
I too am planning on doing load development for 308 with a 165gr pill. IMHO the 165 is the best choice for a single load for all (big game) in this caliber. I hope others chime in, I'm interested in what the popular powders are. I have been burning up some (discontinued RL12) with really good results. I have a box of Nosler 165 BT, that I will work with after shooting up some Speer 170gr FN, those were left overs from loading for 30-30.