Having started to travel to Europe right out of high school, a few points of advice:
I agree with those who advocate for limiting the trip to just 2-3 countries. Or even just one - you could spend years in Italy and still not experience everything, for example.
Although an open-jaw itinerary can be useful, I've enjoyed flying into one city and making side trips from there. For example I recently flew into Prague, stayed for a few days, then went to Austria and back to Prague for a few more days. I found that after I left Prague for a while I had a better idea of what I really wanted to see and had time to do that before I left the continent.
Once you've chosen your destination(s), I found it really worthwhile to learn some of the language (even difficult ones like Czech). You can get by with English, but you'll get better service, assistance, and even make friends by at least trying. Getting decent with pronunciation in order to read menus, etc. can go a long way.
Pack light and be ready to wash clothes (non-iron things especially). A neck pillow, eye mask, and ear plugs are really useful if you're doing hostels and overnight trains.