Food
Of course, long and informative excursions require constant recharging with food and food is the thing about Holy See you should know. It is forbidden to bring food and drink to Vatican museums. However, most of the Vatican area is packed with courtyards and grass-covered parks where you can eat. A great idea to save money is to buy sandwich ingredients at a local store while you're in Rome and stack them while sitting on one of the benches in the Vatican parks. It will also save you time in between the attractions.
If you want to conquer a couple of local Vatican restaurants and do not mind spending time in them, you should choose places less crowded with tourists. But it is worth remembering that the Vatican is a tiny population and every "other" here is a potential tourist and a source of profit, so do not be surprised by some prices in catering establishments.