I would use something in the .270, .308, .30/06 or 7mm mag, range, you may have to shoot at a long range, I have a friend that shot one at 314 yards with an 'o6. We had been at the range and he shot the rifle at 300yds and knew where to hold.
Also, the only thing about using the mosin is I feel like I'd look too much like a noob.
but then again, a kill is a kill wether it be with a rock or a cannon.
It's all about shot placement. What I tell every client is "break them down" if you can break the shoulders you have all day to place a better vital shot! As far as the caliber suggestion I shoot a 25-06 and killed my very first one with a .243 I would suggest a flat caliber slinging at least 120 grains of lead.
.243 to 30-06. If your looking at buying a rifle just for aoudad then you can get away with being picky. Best bet if you ever plan on shooting anything else with it you might want a .270, .308, or 30-06. Those three are very versatile for hunting and ammo is readily available every where from jimbos country store to Academy. Pick a solid rifle with a good reputation and customer service. Remington 700, Savage, Winchester, Marlin, Ruger. Theres even some new budget polymer synthetic models (glock types if you will) hitting the market. Some are reportedly very accurate and smooth while others are a little on the rough side. Do your home work and pick something thats not just a purchase but an investment.