Since the SKS was not designed for precision and more as a battle rifle (repeated shots over a short distance) you will not expect pinpoint accuracy with a military rifle with military ammunition from the era the SKS came from. Not being a handloader I have talked to lots of them locally that say the right bullet weight and powder load will improve accuracy with any rifle, the SKS included.
Remember that the SKS was designed to kill humans. Call a spade a spade the Russians didn't create the SKS to shoot 4 legged animals or shoot steel targets at the range. The rifle was designed in the 1940's/1950's with technology nowhere near even the design of semi auto's 20 years later, designed for semi-auto rapid repeated fire and not aimed/timed shots, designed for rugged piss poor environments (Europe/Asia rain, snow, mud, corrosion, heat, etc.), designed around a cartridge that was small and could be carried in massive quantity in surplus on a soldier's belt/shoulders (because the designers knew this rifle was going to throw a lot of steel), and finally was designed to be CHEAP and PLENTIFUL. None of these factors contribute to an overall accurate rifle. It was designed to hit a 6-8 inch "center mass" object (ie. humans) out to 100 yards.
If you're getting 3-4 inch groups with surplus ammo out to 100 yards standing with irons for an SKS that's very good and you're a very good shot. If you're getting under 2 inch groupings sitting with a gun rest with surplus ammo for an SKS that's REALLY GOOD you're an AMAZING shot! The only problem with both those examples is since surplus is not consistent, you may not get the same result over and over again. Come hunting season with a well made handload or S&B ammo you're going to bag that deer no problem out to 100 yards with your SKS.
Simple things like CLEANING an SKS (which not a lot of people do) and not putting on a plastic tactical or folding stock on it (leaving the wooden one on it came with) will make a big difference for accuracy. A lot of people say the Chinese ones shoot less accurately than the Russian ones. I guess that is up for debate. I will say "yes" the Russians ones do shoot more accurately because a copy of an original design doesn't always perform as well however I have some Chinese SKS's that shoot amazingly well when they are cleaned and the stocks are put tight to the receiver.
If you want an SKS for hunting or accuracy shooting and want to make a "project" out of making this happen, you will have to build one specifically designed for that purpose. Call it your pseudo "match" rifle or hunting SKS rifle. I would pick a Russian one, leave the wooden stock on it, buy one of those receiver covers with the receiver screw claws because once you put it on you're not taking it off, or better yet spend a little more money and buy the one that screws into the receiver itself (totally permanent), put on a really good scope, and only use non-corrosive handloads or commercial ammo with a consistent bullet weight and powder load. With the scope properly mounted and sighted in shooting only one kind of bullet and powder weight will guarantee amazing accuracy over great distances.
Or save your money and time and buy an M14 with a scope mount and scope.
