Hamburg to Budapest by train

DB is the national railway operator in Germany, so its website can be used for booking journeys by German express trains; the ICE and IC trains and it doesn't charge booking fees.
It also sells tickets for journeys by direct trains on all international routes from Germany regardless of whether DB is operating the train service.

It also sells an extensive range of end-to-end journeys which involve making connections both within Germany and in neighboring countries, but journeys between Germany and Britain cannot be booked on DB.

A key feature of DB website worth keeping mind is that it offers 1st class ticket purchasers complimentary seat reservations on journeys both within and to/from Germany.

Seat reservations for daytime in both 1st and 2nd class can also be booked separately from tickets.

Omio is an online ticket agency which offers tickets for rail journeys in France, Germany, Great Britain, Italy and Spain.

The three key advantages of using Omio are

• it offers prices in multiple currencies
• it usually offers price comparison with other modes of travel including flights and buses
• when visiting Europe, you can book journeys in multiple countries in one transaction.

The disadvantage of booking with Omio is that it often adds a booking fee to the final price; therefore when it does so without offering a price advantage, SMTJ doesn't tend to offer Omio as a booking option.

MAV is the national railway operator in Hungary and its newly relaunched website is still at the 'beta' stage, but it can be used to make bookings.
The MAV website also sells tickets for the direct international trains from Hungary and it's booking path for overnight trains is particularly easy to follow.