I agree with the others who have counseled you to carefully clean and preserve this gun since it has a good deal of original finish.
Here's a link to a thread which covered some techniques for bringing out the Damascus pattern in barrels that have a light even patina.
http://www.doublegunshop.com/forums/ubbthreads.php?ubb=showflat&Number=412135&page=1 I still like to gently clean with very fine 0000 steel wool and WD-40. The method mentioned by Stallones using maroon Scotchbrite pads and Palmolive Orange Dish detergent works well too, but you have to be very careful with any Scotchbrite around gun metal. The abrasives in Scotchbrite are hard enough to scratch glass or chrome plating, so they will easily do damage to blued and case colored surfaces.
The wrinkled dirty finish on your stock looks like it might be old shellac. If so, it can be first cleaned with Murphy's oil soap or a solution of household ammonia, then rinsed and dried well. Then, the tricky part is to gently wipe the wrinkled shellac with a small lint free pad saturated in isopropyl or denatured alcohol. Shellac dissolves in alcohol, so you are trying to do a controlled job of dissolving the old finish and re-amalgamate it with the parts that aren't wrinkled. Essentially, you are dissolving and spreading out the original shellac finish. But if you haven't done this before, it is very easy to get carried away and remove the original shellac finish entirely. Not good. I'm hesitant to recommend it for that reason, and suggest that anyone who might wish to try it first practice on junk stocks. A lot of nice old guns have had their value destroyed by good intentions and overly aggressive cleaning.