Mosin Nagants are not going to be as accurate as a modern hunting rifle. But that doesn't mean then cannot be a lot of fun. You can learn considerable gunsmithing at very little risk.
I took a Mosin that I measured the throat in the store (Hornady tool, inexpensive) with little wear on the throat for $140 or so.
Cut off barrel to get it to a shorter length more like 20-22" (barrel ringing is proprortional to I think the 3rd power of the length). Recrowned my horrible hacksaw job with a Lee trimmer cutter until it was perfectly square and perfectly flat (use a 7mm spindle, like for a 7mm08, and shim it with plastic from straws).
Then rework the stock a bit using wood tools to make a flatter forend that will fit a benchrest front rest. Be creative, for crying out loud!
NcStar makes a $40 3-7X scout/pistol type scope that you can attach with dovetail rings to the dovetail that is underneath that Russian rear sight. The Russians didn't alwys cut the dovetail very well, so secure your dovetail rings with JBWeld when you figure out exactly where to put them. All a you guys are always saying you don't need more than 4X, so here you're going to have SEVEN. You will quickly get used to a scout scope....again, you do not HAVE to spend $$$$$$ and be a conformist in life. Your total outlay is now about $180.
If you REALLY want to have some fun, go buy a 3/4" waterpipe from the local home improvement store, and with a cutoff saw, cut a slot to allow your scope mount to pass, heat up some 20-minute JB weld, preposition the correct length of water pipe over the skinny Mosin barrel, stuff something in the bore to protect it, and fill the voids between the Mosin barrel and you sheathing water pipe with JB Weld. You'll need about three tubes of the stuff. You're now up to about $200 invested, and you just performed a homemade barrel sheathing, similar to how the early benchresters used to take a Remington action and sheath it with steel to make it squirm less under recoil. Because barrel ring is proportion to either the 3rd or 4th power of the barrel diameter, and you have now effectively DOUBLED your diameter, you have just considereably reduced your barrel ringing.
I then proceeded to easily hit chest sized gong targets at 600 yards, and occasinally at 800 yards using moderate charges on reloaded brass and Sierra .311 150 grain spire points. Yes, my 7mm08 is more accurate, but then it is well over twice the price and I didn't learn near as much.