The advantage of buying a ticket in advance is that you could get cheaper tickets that are less flexible. However, as they are not flexible, it is not good to use them with a flight arrival.
What I would do (because I definitely would not want to stand after 24 hours of flying) : Buy a "Normalpreis" ticket, which is a fully flexible ticket, with a seat reservation for the train you are most likely to take. On top of that, get stand-alone seat reservations for the next two trains (they should each cost around 4 or 5 Euro). This way you are covered for most possibilities for a little more money. The fully flexible ticket can be used in any case at any time, even if you are delayed by a day or two.
Advantage of buying a ticket in advance is that you can print out the ticket at home and just hop on the train without having to get a ticket at a machine or booth.