I clean my auto .22 with a rod from muzzle to chamber and as stated above, being really careful of the crown. Pull through cleaning systems (cable types) that pull from the chamber to the muzzle would probably be more appropriate. Two things to note, getting a small enough brush to fit in to a 22LR chamber (Otis is good) and pulling a patch rather than pushing usually isn't as effective just do to the mechanics on how it all gets put together. Side note which will get me into trouble (.22LRs are tough little guns, you really don't need to clean them that often) and yes, if your going to park it in the safe for an extended time, a cleaning and lubricating in the barrel is good and you don't need to leave it greasy. A couple oiled patches follwed with a couple dry ones to pull out the excess will do you good.