While I generally buy oils labeled “gun oil”, I’d use sewing machine oil in a heart beat.
These days, synthetic motor oils are probably a good option. I guess the only question would be if the additives in motor oil would be detrimental to firearms in the long one.
For long term storage, grease is an issue as the lubricant evaporates over time leaving the clay carrier. Guns that I do not shoot often but require grease lubrication, I store coated with oil then grease the firearm just before shooting.
Products likke Break Free seem to last well.
WD-40’is not designed to be a lubricant but a moisture displacer.