Use websites like hostelworld.com to research hostels. Read the descriptions and the reviews to get an idea. Some have a frat-party vibe, others are strict about quiet hours. Choose what works for you. Pay attention to location. If it isn't central, you'll spend time and money getting to the center. It's a good idea to have a list of hostels before you go, whether you pre-book or not.
Plan your itinerary carefully, whether you book train tickets in advance or not. For flights, the sooner you buy, the cheaper it'll be. Read carefully and know all the fees before booking. Look at the cabin baggage limits - expect them to be strictly enforced. Figure out how much time it will take to get from place to place. bahn.de is the German train website, use it to find train schedules all over Europe. Be sure to allow time to get from hostel to train station and enough time in the station to find your train.
You will have a locker in the hostel only for the time you are checked in. That's usually from mid-afternoon until mid-morning. On the days of arrival and departure, there may be luggage storage available, but it is very likely to be a closet that many people have access too. Many train stations have secure luggage storage, but it adds costs. If you are traveling in the morning, you have to store your luggage when you get to the next destination, then start sightseeing. If you are traveling later in the day, you have to store your luggage, before sightseeing, then pick it up before continuing your trip. Many sights will not allow entry with a backpack.
I would seriously reconsider taking a large, expensive DSLR on a backpacking trip. It may attract the attention of thieves. A good point-and-shoot camera will take very good photos under nearly all circumstances. If you plan to take a lot of photos, you will want to back them up. Figure out a way, so you don't lose them. Have spare batteries and memory cards so you will always be ready for the next photo op.
Shoes and sandals (you will want sandals when it's hot) need to be comfortable, broken in, and with thick soles or the cobblestones will kill you. I'd bring a sturdy rain poncho, a sun hat, sun glasses and sunscreen.
Switzerland/Italy/Greece. Where? So much to see and do!! How are you getting from Italy to Greece? Are you flying open-jaw into Dublin and out of Athens? If you don't have your flights yet, consider all the advice you get here and work out your itinerary with actual train/flight times before booking to avoid getting messed up with the planning.
Will your plan will work for you? Figure out how much sightseeing time you have in each stop, how much you'll spend on transportation in time and money and decide if it's worth it or if you want to cover less distance. For instance, you could see small towns between big cities. Or take day trips without changing locations.