Rather than using any kind of grease, use plain old wax. grease can get into the wood of your stock and can cause problems. You can use an automobile paste wax or floor paste wax. De-grease your barrel and then put on three or four coats leaving time for the wax to dry between coats. Polish your barrel after each coat and buff to a shine. This will produce a long lasting protective coating. At the same time, put some wax in the barrel channel to protect the wood. Several coats there as well done the same way. Wax applied to these areas will protect your barrel and stock from water damage. Of course, it is up to you to try your best not to get water in the barrel channel in the first place. But, a good wax job will give you some long protection. Forget the grease idea 'cause it ain't a good one. Use wax. :thumbsup:
I like to apply a light coat of paste wax to the outside of my stock and buff it every time I clean my gun. It is just part of my routine cleaning procedure. This just protects my stocks and keeps them looking good.