This pic is just started toward filling the grain, just two coats of wet sanded Danish oil, two with linseed in the blend. It's an older sheridan, you can see how the linseed has warmed the black walnut, and accented the color and grain.
Linseed is a traditional oil finish for guns for several reasons...it enhances color and grain, it's cheap, and its easy to apply and touch up.It also rewards attention to detail and time invest
The best finishes at excluding moisture (like polyurethane) are often not the best for other reasons(appearance and easy repair are two)but whatever the finish is, ALL surfaces need to be sealed as well as possible.
Oil doesn't dry, or just soak in, it polymerizes, the molecules link up into longer chains. Certain chemicals catalyze and speed this process, as does heat and UV light. "Boiled"linseed oil has hardeners added, as do all oil finishes (varnish is an oil finish with extra hardeners)
How "deep"(and it's only a small fraction of an inch unless you use a vacuum chamber)an oil finish penetrates is mostly controlled by viscosity...water thin finishes will penetrate deeper than thicker ones. Since most oil finishes are compatible, I like to use a very thin one like danish oil to start a gunstock finish,using it straight for the first several treatments, wet sanding with increasingly fine grit, then adding boiled linseed to help fill the grain and build the finish faster, after I'm done sanding. After several rubbed in coats of the thicker oil(about 50/50 linseed/danish)have cured, I'll go back with 800 grit paper in a semi rigid pad, wetted with straight danish oil. This will level the finish better than the usual 0000 steel wool.
Note...when you wet sand with the Watco, you make a "mud" that fills the pores...let it sit until tacky, then scrub off across the grain with a an old towel or similar
Linseed also has the advantage of warming the color of the wood(it's a light honey shade)and accenting the grain and shimmer more than anything else I've tried over the decades. Tung oil, for instance is clear, and doesn't seem to pop the figure like linseed.