A Finnish M39 is tremendously accurate, if you can a) find one, and b) find one that hasn't been shot out.
I have a pretty little Argentine Mauser, built at DWM in Berlin in 1897. Shoots like a dream and looks like it came out of the factory yesterday, except for the arsenal work on the stock that converted it from artillery to cavalry configuration. Accurate as all get-out.
I've known people who look down on old battle rifles for hunting, fearing that they aren't precise enough to be humane(!). But good luck getting better than 3 MOA out of a Winchester '94 at 150 yards, and a lot of Americans have put meat on the table with that iconic gun, and plenty of vets coming back from the world wars kept their family in meat with battle rifles.
I have found that almost all rifles and pistols are more accurate than the guy or gal on the trigger. To wit} They will hit what and where they are aimed. The guy or gal on the trigger blames the rifle or pistol when, in reality, they are who is at fault. The ones I have will knock a gnat’s eye out if aimed correctly.