The first fixes I'd do to the rifle wouldn't be to the rifle. I'd put it on decent front and rear bags. See how it shoots like that before you start your tinkering with the rifle itself. Then try some different factory ammo - some of the high quality stuff. And yes, tighten all the hardware snugly. Scorch's suggestion about taking off the bipod sounds like a good idea once you have the shooting bags.
As for replacement stocks, I have one of the Hogue stocks on a rifle. Great stock for shooting, but it is kind of heavy. Next stock I buy, though I don't know which make I would choose, would be synthetic, attractive, and very light. I think that also means it'll be very expensive.