If you go to Rome. Any hostel close to the Termini Terminal. will be around 14 to 20 euros per night.
Train from Airport to Termini Terminal 12 euros.
Must of the tourist places are free... Vatican Museum and some other places charges u about 6 euro.
Panini 1 to 2 euros = Bread with NICE NICE Ham inside
Birra Moretti or Boffa D Oro 2 to 3 euro. you can drink while walking the town.
Metro and Buses about 1 euro, but you can purchase the ticket and keep it in your pocket as the romans never validate, "convalit" the tickets... When in Rome...

If you are going out drinks will be aroun 7 euros, beers 5 euros, and house wine 2 I will go for the house wine.

If you are planning to see the pope he only rock the vatican on Wednesday and Sundays.
The Sixteenth Chapel has funny schedules, check that one first as the other things are open always...
Have fun and enjoy your trip. Italy is full of fun.