Anytime you have the gun out, make sure you wipe it down after handling. Smokeless powder will not harm the barrel if left fouled, but at the same time you are not doing the gun any favors. The 870 breaks down very quickly and easily. After shooting it I would break it down, and clean it with a good solvent (hoppes, shooters choice, etc.) The mopps are used to run the solvent down the bore, followed by a scrub brush if neccessary (probably not after only 30 shots, but we shall see). Follow with a dry mop or a few thick patches (I use old cotton T shirts) until the bore is shiny. It should be as shiny as a mirror looking down. If there are streaks, that needs to be scrubbed out with the brush.
Many people minimize the care thier guns get, and the results over time is junk. A good gun used with care, with a few minutes of TLC at the end of the day will last for generations.
It is mornal to get some finish wearing on the magazine tube, and occaissionaly on the bottom of the barrel. I no longer have an 870, and cant remember if I had wear there.