You take the train from Rostock to Hamburg I assume. You could continue your trip by public transportation. S1 (S-Bahn) goes directly to the airport. 35 minutes, frequent trains. The S1 starts at one end of the city, goes through the center and the main train station and then to Poppenbuettel at the other end. Part of the train will go to the airport instead of Poppenbuettel.
I hope an expert will come here with precise English language instructions for tickets and which carriages of the S1 train to take.
If you are arriving by train then taking a taxi to the airport makes no sense at all.
2) Walking to the taxi rank will take longer than walking to the train
3) The journey is likely to be quicker by train
Not needed. As no matter which station you buy to you'll get with this distance a ticket to "Hamburg", i.e. a ticket good to any train (incl. S-Bahn) station in Hamburg.
There are S-Bahn trains of the line S1 every 10 minutes to the airport. Note that only a part of the S1 trains go to the airport - but this part is clearly marked.
Thanks for fare information. I am familiar with buying tickets to Hamburg Airport using regional trains from places in Schleswig-Holstein (where a ticket to "Hamburg" always means "anywhere within the central zones"), I wasn't sure what the situation was with journeys from further afield or journeys that involve IC/ICE trains. Now I know!
It actually works that way in almost all cities, Aviatrix.
Here‘s the official list for „same fare“ stations for your reference:
It's not the same train. You change trains at Hamburg Hauptbahnhof (Central Station). But it's simply a case of getting off one train and onto another, and your ticket covers the whole journey.