The finish on an 0 Grade would be shellac, the checkering would be flat topped not pointed. If it were mine, I would look again at the checkering, clean it with alcohol and a toothbrush, then clean the stock with the same. Apply a few coats of amber shellac staying out of the checkering. Then I would put some shellac on a toothbrush and lightly go over the checkering.
On the metal finishes, use 0000 steel wool with some oil on it and lightly go over the rusted areas. It will come off it like you said it is lightly rusted.
Since you inherited this gun, I would not refinish it, as it shows how it was used in the past and why take that away from it, just clean it up.
