You can find a nice apartment for a reasonable price in Austria if you take your time and do some preparation before you start looking. This Just Landed article will give you an overview of what to expect and how to plan your search.
The rental market is well developed in Austria; you will find a broad range of offers from very old buildings with a lot of ‘character’ up to brand-new, very comfortable flats. First, try to get a feeling for where you would like to live. City centres are crowded and expensive. Outside the centres, housing is cheaper; you are closer to nature and may still be able to reach the city in a short time by using public transport. Apartment prices vary greatly depending on the area in the respective city. For example, in the outer districts of Vienna you will easily spot the difference (are there only luxury cars parked on the streets?) and be able to guess the appropriate price range. Walk around and try to get an impression of what the area is like. Then check the public transport (Metro, Bus, Train) and how long it will take you to reach your workplace, university or points of interest.
Many students live in shared apartments. There tends to be a relatively higher turnover of free rooms, so there is a fair chance you find a room in a shared apartment quickly.
Austria has a relatively expensive cost of living. It is cheaper than Switzerland or Nordic countries, but more expensive than Spain or Italy. In the countryside everything is cheaper, but it is more likely you will live and work in Vienna or one of the other larger cities. As a single person you should calculate around €1400 as a monthly budget to have a comfortable life. Apartment prices start at around €400 per month for rent, excluding utilities.