If you are all on one ticket, you should be able to check your bag through to Naples. When you check in for your first flight, make sure your tag says NAP.
If you are not all on one ticket, show them the various tickets and ask if they will check bags to Naples. Reports here indicate that even if you are told in advance that they will not, they sometimes will at the airport itself.
Assuming your bags are tagged NAP, you will not see them until Naples. You will go through customs in Naples, but this is merely a matter of walking through the "Green Channel - Nothing To Declare" line. Unless you are "randomly selected for additional screening (rare but possible), you're done.
You will go through passport control on your first entry to the Schengen zone. If you post your entire itinerary, we can give more details.
I agree with Frank that you should have 2 days of clothes in your carry-on, but that's not just for this itinerary - that's for any time bags are checked. And if you have extra space in the carry-on, bring more underwear. You can re-wear clothes more easily then underwear, if your bags are seriously delayed for any reason.