168gn-175gn smk federal gold metal match or black hills.
Should show you what the rifle will do. The bullets come in a tipped match king and I would hunt with it.
Just punching paper I'd buy bulk fmj and/o rmatch ammo and break the barrel in. My go to factory round is Federal Gold Medal GM308M with the 168gr Sierra Matchking bullet. For hunting pick up a few boxes and see what your rifle likes best.
I've got one in .308 also. Sweet shooter. Likes Sierra 168gr with 45gr of Varget or 44.5gr of IMR 4064. Can't go wrong with Sako..my opinion it's the best production rifle made