Modern stainless barrels are much less susceptible to rust and corrosion, especially if the times between shooting are within a couple of weeks. Nevertheless, a thin film of some kind of oil will not hurt, and if it is really thin, there is no need to try to wipe dried oil out of the barrel before shooting.
My preference is to polish all my new guns' bores before I first shoot them. I use a bore paste, lots of patches, and 20-30 minutes of elbow grease. A smooth bore fouls less and is easier to clean. I clean the bore well after polishing it. Then I use a lubricant that binds to the metal rather than just laying on top of it. I use Militec-1. I swab it well, let it sit a few minutes, then dry patch out the excess. Then I put a pistol barrel in the oven at low temp (150-170 degrees) for 20 minutes. This helps bond the lubricant into the metal.
Thereafter, I can clean a bore easily in just a few minutes. If I am going to shoot that gun again soon, I'm done. If it's going into storage, I run a patch with a few drops of the same oil though the bore. I never wipe it out before shooting.