Where can I get a correct stock?
Ebay. $200 if you watch closely.
You do not want to do any bluing. The second you touch that gun, you have nothing. Any "fully restored" scenarios delivers you a gun worth ~$500, even if you throw $1000 at it.
Right now, the gun isn't yet irrevocably ruined...but you're one decision away from owning a $400 action for a custom build.
Don't reblue. Clean with 0000 bronze wool and oil to remove surface rust.
Don't checker...that isn't the original stock or it has had its checkering removed. You need an unrestored, slightly worn original 1955 era stock.
Don't put the wrong folding leaf sight back. The correct one exists for $35 if you search.
Do put on good, and big mounts. I recommend Talley mounts or if you want to spend more, do EAW pivot mounts. It will cover the bluing blemishes on the bridge.
Fully cleaned with correct stock, correct leaf sight, and scope mounts put on it. (scope and rings not necessary) you will have a $1400-$1600 gun. Any "restoring" versus "conserving" will give you something near worthless. (parts for a custom build)
Labor, +$300-$500 in parts, = $1400-$1600 gun.
Restoration, + more bad decisions = Parts gun. Action worth $400, rest of it flea market bits to sell off here and there.