Hey, I'm in Gr.11 and I went to Europe 2 summers ago and basically planned alot of it by myself! My parents went with me and survived so I guess I have some credibility! :) I'll be calculating cost/person unless otherwise specified.
Plane ticket (Go in June or August -> when costs dip slightly): $800-$1100 (My family flew from Canada to Rome and back from Barcelona for $2100 for all three of us!)
Lodging: hotel or hostel? Hotels: 65-90 euros/night for 2. (Search Accor Hotels, they have budget to decent to luxury hotels in Europe <- very clean and well maintained) Hostel - 14 - 30 euros/night
Food: Try to find hotels which offer free breakfast (preferably buffet): 30 euros for lunch and dinner/day.
Tickets to attractions: 30 euros/day
Domestic Travel: By train -> for one month, its better to by a rail pass. Don't overlook plane tickets. Some go as cheap as 1 euro plus tax!
In city travel: 10 Euro/day -> try walking, you explore and see so much more. If its too far, take public transit, its a sense of adventure. If it's desperately far or late at night, take a cab.
Extra costs: $10 Euro/day
Bottom Line: The total cost will depend on when and where you splurge. My family did our 2week trip for $8000 CAD. We visited Rome, Venice, Vienna, Berlin, Copehagen, Paris, Barcelona and a 5 day cruise in the middle. We were frugal but did not starve ourselves. We gained 4 pounds during the cruise in the middle! Roughly speaking, expect to spend at least 3500 euros!
Hope it helped!