I usually shoot the cheap federal power-shok through mine. Wal-mart has it for about $12 per 20, only slightly more than wolf, and it is pretty good quality stuff.
That being said, I shoot wolf 7.62x39 through my other saiga and I've never had any problems.. Usually the AK platforms are fine at eating up whatever you give them, I don't think the .308 would be any different, but you might not get the accuracy you want.
This rifle will work fine for your uses. Just don't expect bolt action accuracy, I've never done any official testing, but I probably get about 2-3 moa using the federal, if I am shooting well. I can get shots within an inch at 50 yards. Plenty well enough for deer and target shooting.