If the fibers of the wood have been cut, as opposed to being dented, then the wood cannot be raised at that point. If just depressed or dented you can try placing a damp cloth (after the finish has been removed) over the damaged area and a hot iron over that. The steam generated can sometimes swell the wood back to its original level. As for the finish you should probably read up on the subject & determine what you want prior to attempting. Most large book stores have books that cover the subject.
We have specialized in stock restoration and repair for 20+ years and have done a couple of Beretta Silver Snipes. I personally own one that my father gave me when I was 16 so I will go to some extra length to help you out here.
The first precaution I can offer is that when you remove the butt stock be sure to use masking tape around the screwdriver shaft. Build up the diameter of the shaft to insure that it centers with the bored hole in the stock to prevent the screwdriver bit from jumping off of the screw head as it will become wedged and split your stock. There are no replacement stocks currently available and it would be relatively expensive to have it duplicated and checkered. The wood finish process used by Beretta included a wood stain applied prior to the finish unlike the pre 64 Remingtons and Winchester that had the stain in the finish. I would suggest Laurel Mountain Forge stain (walnut) if you are trying to achieve the original color but an old English red looks very nice. For finish I would suggest Classic Gun stock Finish by Pilkington. Both can be purchased from Brownells. Be sure and closely follow the 1000 word instructions that come with the finish.
Strip the old finish then wash the wood down a couple times with lacquer thinner. Whisker the wood by wetting it with distilled water which will raise the grain. Cut the wiskers off with 400 grip gold paper. You can raise any dents where the wood fibers are not broken with a cloth wetted with distilled water and an iron applied on top. The steam will raise the dents as wood fibers have a memory. Any gouges can be filled with walnut wood filler. You may have to gain the repairs with a gaining pencil to help blend them. Stain the wood and apply the finish per the directions that comes with the Pilkington finish. It is a sanded in finish meaning you will be filling the grain as you apply the finish in multiple coats. If you don't use Pilkington's you may need to use grain filler (walnut color) before staining. Lastly, during the wood refinishing process would be a good time to have the metal re-blued if it requires it. The Beretta Silver Snipe had a rust blue rather than a dip and ship hot blue. Rust blue is more expensive but much more durable. Good luck with your restorations.