I would look around online for a ticket, and be flexible about the starting point unless you have very specific interests. Get yourself dropped into a major airport and just hit the ground running. Unless you have a personality where you need to have accomodation reserved in advance, etc, I wouldn’t make any real plans for your itinerary.

Get a backpack, lighweight sturdy clothes, and good shoes. You don’t need to pack for the Yukon, just bring things you’d need for overnight plus a few days of clothes. Make sure the pack is comfortable and there’s room for presents to bring back afterwards. Get a Lonely Planet or Rough Guide book for the areas you’re interested in, and sketch out scenarios, but don’t obligate yourself to this. Bring 1-2 friends who have similar outlook to yours, but traveling alone can be even better, especially if you are somewhat congenial don’t mind making friends on the spot with fellow travelers.

One thing I would suggest is that unless you like to plan everything ahead of time, don’t buy a Eurorail pass, or a Hostel card, etc. If you’re a student, you may be forced to buy a student id card of some kind in order to get a cheap student airline ticket, but you’ll probably never use it. Think of it as a tax. The way to save money moving around within Europe is to just look for the cheapest fare on the bus or train to get from your current location to wherever you decide to go next. Typically you’ll meet fellow travelers who can give you really good advice about where to go next and how to get there. You’ll have too many places to go/things to do, so let cheapness be your guide.

That takes care of travel. Next food then accomodation. For food, you can usually afford to eat 1/meal at a restaurant per day even if you’re pretty cheap. When you do, go for the daily set menu at a local cafe and you’ll usually be pleased. For breakfast, and for lunch or dinner, buy groceries: bread and sandwich fixings. As you travel the bread, cheese, meat, and veggies will constantly change so you won’t be bored. You can usually buy pastries on the street, and coffee, and ice cream, and these can all be very cheap considering how good they are.

Finally accomodation. When you get into a town, ignore people who try to talk you into going with them to whatever hostel or tourist office they claim to represent. You will run into these people in esp. Eastern Europe. If you are willing to pay a little extra, you can find the official tourist information and get a recommendation, but keep in mind that the hostel, pensions, and 1-2 star hotels who sign up with these offices have to pay for it. You can cut out the middleman by walking around and negotiating. Always see the room. I wouldn’t rule out hostels or pensions or 1-2 star hotels, they can all be good, depending, you just have to see. Alway ask for a student discount even if you are not a student but would pass for one.

If you’re traveling on a bike, this is all easier: travel is free, but you can still put your bike on many buses or trains. And it is easier to scout out neighborhoods for restaurants and accomodation. I backpacked on foot around Europe a few times, and by car, and by bike. Bike is my favorite way, but you need to get a solid frame and wheels, and pannieres, and be willing to gut it out. But the great thing about biking in Europe is that you don’t have to wear a pack on your back, you can dart around in cities, you’ll be in great shape, and you can wander into remote areas and always find another village every 5k with friendly people and great food.

Let me know if I was helpful, or if you have more specific questions.