We were on a small budget for several days in Rome, and I can recommend the Roma Pass that includes transportation. It payed off for us. Even after several trips to Rome, we rode a lot of busses and saw more far ranging parts of the city with our passes.

You did mention campgrounds. Most posters here travel in 2 to 4* accomodations in Italy. You might want to try your questions on ThornTree, or the message boards at Rick Steves' site. Those sites have more bare bones budget travelers than does this. Google for links.

If you can do shared bathrooms, that opens another range of budget accommodations. I generally don't even look at a place with shared baths, because I wouldn't want to share a bath, but if you are willing to stay in campgrounds, I don't think shared baths would be a problem.

Buying fruit in markets should help. Don't buy bottled water, but carry a bottle to fill when needed.

Busses in Italy can be inexpensive, and in some areas, are a decent way to get from place to place. Otherwise, you will be using trains. But we don't mind a bus in Italy. We have used them in Tuscany, Campania, the Veneto, Lazio.