In Austria the train network works very well and the ÖBB is one of the most punctual rail companies in Europe. But if you come unprepared the prices can be quite high and there are easy options to reduce it: as an standard example let´s take Linz Vienna. Standard ticket is around 40 euros, if you have the Vorteilscard (which costs 20 euros for under 27, 69€ for adults, you can buy it just before your trip and citizenship or residence do not matter) the price is down to 20€. If you are early in advance you can get a Sparschiene (early bird) ticket and get the same track for 9€, this is just bound to a specific train and name and there are certain contingents.
Confusing and challening might be if you have your end or start point in a different country, every national railway company has different, although similar, offers and it could be that for Munich-Linz the DB ealry bird is cheaper than ÖBB because of a special offer. If you go via i.e. Czech Rep a early bird ticket might be half the price from the ÖBB, so take the time and compare. Standard tickets are quite often the same but early birds are differing.
Tickets can all be bought online and with print at home and often also just in the app and to be shown on smartphones so it is very relaxed. In addition at machines they sell the same tickets.
Several trips I a showing you here are perfectly suitable for trains. If you want to start your own planning or even want to combine hiking and interrail here some basic information to start with: the fastest trains in Austria are Railjets and several also pass mountain areas. Especially from Salzburg and Innsbruck there are great and close connections to choose from. The Railjet Salzburg Klagenfurt for example passes: Abtenau, Bischofshofen, St. Johann/Pongau, Bad Gastein, Mallnitz, Millstätter See. All are hiking destinations and so you can reach in like 90min from Salzburg the begin of your trip.
The railjet from Vienna to Bregenz stops in Tyrol at the begin of all major valleys, there usually connection buses are waiting and you can go into the valleys. In 6-7 hours you will make it into several valleys, if you start early there is even enough time for a half day hike or for the ascent to a hut to sleep over there (they usually take between 2-4h), in summer you just need to keep in mind that in the afternoons the danger of thunderstorms are rising so it is definitely advised to start early and check the weather forecast. Zillertal, Stubaital, Wipptal, Ötztal, Pitztal are all easy to reach with one time changing. From Innsbruck to Sellraintal or Nordkette it is even closer, starting from Salzburg or Linz saves you another hour or 2 so quite convenient access. For weather forecast you can use this. Check the right federal state, the pictures and then either with some German knowledge or translate program you will do it!
Keep in mind that in the mountains it might happen that in one valley is big thunder and in the next there is nothing, so apps showing you the forecast for the exact location are often not accurate and you should not trust them too much, rather expect the worst to be prepared (rain jackets, leaving early to avoid thunder, do not go on ferratas with possible bolts).
Information to follow
Huts: most huts are owned by the Alpenverein or Naturfreunde in Austria. If you are member of either of them you get discounts (appr. 10€ per night) and maybe more importantly an insurance for possible accidents and helicopter rescue (and you also support the associations with their work providing and maintaining huts, hiking paths, events and protecting the alpine area. Information in English about the insurance, Naturfreunde has a student´s discount whereas Alpenverein is the bigger association and their membership is also accepted in other countries (Italy, CH, Germany) for discount.