Three different products get called gun oil and they do not do the same job. Buying the wrong one is the commonest mistake on this page.
Lubricating oil goes on bearing surfaces — hinge pin, bolt, action, ejector work. Napier Gun Oil, the Bisley drop tin and Browning's Legia spray are all in this group. A drop tin gives you control; an aerosol is faster but easy to over-apply, and oil that runs into a wooden head will soften it over a season.
Rust preventers such as Birchwood Casey Barricade and Parker-Hale Young's 303 are for storage and for wiping down barrels after a wet day. They are what goes on the gun before it goes in the cabinet, not what goes on the moving parts.
Stock finishing oil — Phillips English Walnut Oil — is a finish for bare or tired woodwork. It is not a lubricant and should not go near the action.
If the gun has been out in rain, clean and dry it before any oil goes on: oil over water traps the water underneath.
Related: cleaning kits · gun care · gun cabinets