[I haven't started my degree yet, but I already got accepted into the university that I picked (UNSW), so I still count... right?]
Prestige was definitely one factor that I considered. Even though I also believe that prestige is rather overrated, I do acknowledge that a university's prestige can partly (however minute) end up affecting what job you end up getting in the future, so I had to consider it. I eventually chose UNSW because of its great reputation for its Commerce programs and its place on the QS World University Rankings list.
The location was also another factor. I grew up in Hong Kong (international student), so I'm awfully used to all of the conveniences of the city. Since UNSW's located in the city, I won't miss any of those conveniences, which is great. Its location also means that I won't have to put up with long travelling times or high transportation fees. As you can tell, the location was quite an important factor for me.
My age was another factor that I had to consider. Since I'll be under 18 by the time I enter university, I had to see which universities would accept international students under the age of 18. That ruled out universities like the University of Sydney.
The cost factor is another big one that I considered. When I got to this factor, I pretty much eliminated every university out of my list except for the University of Melbourne. I ended up choosing UNSW because going to UNSW for a double degree is still cheaper than going to the University of Melbourne for a single degree.
...y'know, I'd like to ramble on and on about my reasons why, but I can't remember any other reasons why, haha. So there you go - 4 reasons why I chose UNSW.