Brand new I'd disassemble, clean, and degrease the entire shotgun inside and out all except for the trigger group which I'd leave in tact.
For the trigger groups I use a can of Birchwood Casey 'Gun Scrubber'. This can be found at most any sporting goods store, WalMart, etc. It's a pressurized solvent that when applied with the included thin red tube has enough pressure to get down in the little cracks and crevasses between all the small trigger parts to blow out any grease or fouling once it's been used for a while. Safety glasses are recommended when using this solvent as it really burns when it accidentally gets in your eyes. Not going to tell you how I know that. It air dries fast on it's own, so there's no need to wipe off any excess solvent. Once it's dry I apply a minimal amount of Rem Oil with a cutip to all the internal metal surfaces and moving parts, paying particular attention to any surfaces where metal contacts metal. Once applied, I wipe off any excess with the dry side of the cutip. Too much oil or lubricant will only attract and gather fouling which will make subsequent cleanings more time consuming.
I use the same Gun Scrubber solvent to clean and degrease the rest of the shotgun. Mossberg has a tendency to cake their firearms with preservative before shipping. This factory grease is very thick and sticky. It attracts all kinds of grit and fouling, so making sure to remove it all will go a long way toward ensuring proper function. I spray the solvent on each part and rub with a toothbrush to break up any solid clumps. After that I apply a bit more solvent and wipe down with a rag, then repeat as necessary until the parts are squeaky clean.
Once everything is clean I like to use Birchwood Casey 'Barricade' to coat, seal, and protect the metal surfaces from rust. This is particularly important for the barrel and any small steel parts. The receiver is aluminum, which does not rust, so application is not needed there. Apply sparingly and wipe off any excess. Next I apply a small amount of Rem Oil to the surface of any moving parts that make contact with metal. Again, not much is needed and any excess should be wiped clean.
After all that, you're ready to reassemble and go shoot. I typically only clean my pump guns once a year and that's really only if I get bored. The only reason to clean them any more often would be if the action starts binding or sticking due to a buildup of fouling. I have a habit of running a bore snake through the barrel at the end of every range trip, while the barrel is still warm before I case the weapon for the trip home. This helps keep buildup in the barrel to a minimum by removing carbon and lead before it has a chance to fully cool and harden. I run the bore snake through the barrel at the start of every range trip as well. This ritual helps ensure that the barrel is clear of any debris and is safe to fire.
Please post up if you have any questions or need any further detail. Enjoy the experience, and be sure to let us know how it goes...