I would like to visit Venice, Monte Argentario, Como, Napoli, and Sicily
Italy is not the cheapest of options and the places that you wish to go to can be expensive, particularly in the high season.
I would suggest that you look at hostels, camping or renting a small apartment if you are going to be in one place for a while.
For getting around, you could get a rail pass but its probably as cheap to get the tickets direct at the station. The rail network is great in Italy and well worth using.
For food I would suggest that you go to local markets and do as much as you can yourself - buy ham, tomatoes, bread and make sandwiches etc and perhaps stick to a fixed menu in the evening where you usually get 3 courses plus a glass of wine.
Of course, if you are in a hostel or similar, then you can do a lot of your own cooking which will definitely cut down the costs. Seek out the restaurants that are off the beaten/tourist track and you will definitely get more for your money.
I would suggest that you dont stay in Venice itself (unless you can get a great deal) but perhaps consider staying outside of Venice and catching the train or bus into it. Much cheaper lodgings would be available. about 7 years ago