Frankfurt to Klagenfurt 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.

OBB is the national rail operator and its booking service offers journeys by express trains within Austria, as well as international journeys which don't involve making a connection outside of Austria.

It pays off to book online, as the discounted 'Sparscheine' tickets are only ever made available on the website, and when making international journeys to and from Austria, these Sparscheine tickets tend to be cheaper.
OBB can offer particularly good value for money when travelling with children on international rail journeys, but something to watch out for when travelling between Austria and Germany on daytime trains, is that reservations are an optional extra; but if you book 1st class tickets with the Germany railways website DB, the reservations are complimentary.

OBB often takes a unique approach to its booking path, but a key thing to keep in mind is that the first price you will see for any journey is that of a Second Class seat.
The costs of upgrading to first class, a reservation, or a sleeping cabin etc, is then added to this price.