Below is the collection of websites I used during trip planning.
http://booking.com I like using bookings.com to search for hotel because the prices in search result include tax and fees. This allows better comparison across hotels.
http://hotel.com Hotel.com has a loyalty program where you can get one night free after booking 10 nights with them. Usually, I would search for hotels in bookings.com, then plug in the hotel name in hotel.com to compare prices.
http://airbnb.com Apartment rental. I like using airbnb in the middle of a long trip so that I can do laundry. I would be careful and choose rentals that have at least 20 positive reviews. It’s also a good idea to google the street view of the apartment to get an idea of what the area looks like.
Train tickets: http://seat61.com This site has everything you need to know about traveling by rail in Europe. To get the cheapest rail tickets, you should buy rail tickets as soon as they come out, which could be 3-4 months depending on the countries you are traveling in. Buy directly from the country’s rail website (use seat61.com to figure out which website you should use), not Raileurope.com as they charge extra fees.