What I've done on my rifles is to give the metal that's not exposed a double coat of Johnson's paste wax and renew it from time to time as it's convenient.
The barrel channel, inlets and inside of the stocks get a good coat of boiled linseed oil thinned 50/50 with turpentine to do the same thing. When I get a rifle, all the metal comes off, every bit of it, so the stock can get the thinned linseed oil on and in every nook and cranny including inside the wedge key channels, ramrod hole and screw holes. Then it sets overnight to dry before reassembly. Anyplace likely to get wet, like under the buttplate, gets a double coat.
I've never liked the idea of greasing wood. Eventually the grease softens and degrades it. But what do I know? I only built and repaired wooden boats for 40 years and met John Wayne when I replaced some planks in his 110' minesweeper, the Wild Goose.
Three Hawks