You should always oil your rifle after cleaning it with chemicals. Once more, only a very thin layer of oil is required. A dry patch should always be ran twice through the barrel after any lubrication.
Before you fire the first shot, make sure to clean off your gun once more if it has been in long-term storage.
Switch to passing a patch through the barrel lightly lubricated. Use gun lubricant designed especially for use with weapons.
After that, repeat the process by forcing a brand-new, dry patch through the bore a few times. This will do more than just prevent rust. Running those areas through could remove dirt and tiny insects that got into your gun's barrel.
If you intend to keep your firearms in storage for an extended amount of time, applying a very thin layer of oil to the barrel will be extremely beneficial. It can also aid in neutralizing any solvents that may still be present in the barrel after cleaning.