The 308 Win. is my deer cartridge of choice. Has been for over 40 years. I have taken deer cleanly for near point blank (30-40 yards) out to about 400. I dropped a very nice Montana mule deer at about 325. I have also killed several feral hogs and a few varmints with my set up. As others have already stated, there are tons of good choices of factory ammo. One or more should group fine out of your set up. I hand load for mine, but have used several factory loads along the way.
My favorite factory load for my 308 Win. (a Styer rifle) is a particular Federal Premium, because it groups great in my rifle and has been consistent lot to lot. This particular ammo uses the 165 gr. Sierra "Game King" bullet. In my hand loads, I use the Nosler "Partition", 165 gr.