[Ron Wood]

You have a pretty nice example that has the early "one screw" stock, i.e. the stock iron is attached to the stock with ony one screw. This feature is considered a bit of a premium over the later and more numerous two screw stocks. The leather case appears contemporary to the carbine and is a somewhat rare accessory in its own right.
No attempt should be made to "restore" or refinish any of the rig (gun, stock, case). Just judicious and careful cleaning is all that should be done to preserve its value. Professional removal and cleaning of the stock iron plus replacement/restoration of the screw might be considered without diminishing the value, but it is not really necessary.
Congratulations on having a fine family heirloom.