There are two ways of approaching a Backpacking Trip and both of them have their pros and their cons.
The first one is to plan and organize everything from the first day to the last day and make all bookings in advance (transport and accommodation). The advantage is that you won’t have trouble finding transport or accommodation and you will get them for a very good price. Transport, especially trains in Europe or flights, get more expensive as closer you book to the travel date, so booking in advance is much cheaper. The same thing can happen to hotels or hostels. But this is not the only reason for booking accommodation in advance. As later you book your place to stay as more likely it is that all good and cheap places are already booked – so you will have to find a more expensive alternative. The disadvantage of planning everything in advance is that it’s difficult for you to change plans. If you like a city and would like to stay longer or if you don’t like a place and would like to leave earlier it might get complicated with the bookings. Although there are options to book with free cancellation for example.
The second option is the exact opposite: not plan anything and go with the flow. Therefore the pros and cons are inverted. The advantage is that you can decide where and how long to stay spontaneously without having any trouble canceling hostels, buses, etc. It also gives you the possibility to follow other people’s recommendations that you meet on the way. The disadvantage is that you might have to spend much more money because as already mentioned transport usually gets more expensive as closer to the travel date and cheap places to stay may already be booked.
So what to do then? I recommend you find a middle way. You can maybe plan your trip one week ahead and book with the option of canceling and getting your money back.
We usually stayed in hostels. Compared to other regions of the world, like Southeast Asia or Latin America, hostels are more expensive in Europe. We spent between 7€ (in Vienna) and 15€ (in Venice) per night. There are also other options like Airbnb or Couchsurfing.
We traveled mainly by train and bus. Europe is very well connected by land. Also, you won’t have any problems with passport and luggage controls if you travel inside the European Union which is amazing, to be honest. On top of that transport is pretty cheap in Europe (we got many buses and trains for 5-10€).
I always recommend people eat local food when they travel. Eating out is quite expensive in Europe though, especially in tourist cities (Rome, London, Paris, Madrid). A cheap meal would be everything that you can get for under 10€. Street food or snacks (for breakfast or dinner) are also available for less. Still, I think you will spend between 15-20€ per day on food. If you want to make it cheaper you can buy food from the supermarket and cook in your accommodation.
We tried to visit as many places as possible. In European cities, you can usually just walk from monument to monument (so you won’t need to pay much to get around) or take public transport (which is expensive compared to other regions of the world but still affordable). Entrance fees can be cheap (3-5€) or expensive (30€+). You should always decide if you think it’s worth it and also remember that you might visit this place only once in your lifetime.
The daily budget in Europe might be higher than in Southeast Asia or Latin America. We spent a minimum of 30-40€ each day including accommodation, transport, food, sights, and tours. And I think we managed pretty well. I have heard people saying that they spend 50-100€ per day.