Good shoes, rain protection and binoculars
If you want to stay in Norcia and might need to park “outisde” or walk from train/bus stations to your accommodation, I would recomment that you bring luggage on wheels or backpacks, they are easier to carry on the often cobblestoned roads. Definitely bring shoes with which you are comfortable for walking. Norcia, although small, has a lot of cobblestones. Your feet will be grateful in the evening. Bring warm clothes, even in summer, as the temperature might drop in evenings. Umbrella or raincoat might be a good idea, depending on the season. I needed good rainprotection in April (2008). If you want to visit churches, bring something to cover arms and legs, as you might not be let in with unappropriate clothes.
If you want to hike in Piano Grande and its surroundings, bring hiking boots (ankle protection). There are enough pharmacies where you can get medical supply. Bring translation for prescriptions. You might like to bring first aid kits with band-aid, as you might have blisters from walking. Foot cream is a good idea, too. My feet were happy in the evening with this The most magic impressions throughout whole Umbria and Norcia of course are the churches and other buildings. Many of them have ornaments, sculptures and other details where you would need a good tele lens. % If you plan to hike, bring all your equipment, as it is most unlikely to find places where you can rent tents and the other stuff. Binoculars are a good idea, for wildlife watching or looking at the building details. Maybe a torch as well, as depending where you go, streets might not be lit appropriately. Italian dictionary is also a good idea.