I was in Taiwan earlier in the year for a holiday including one week in Taipei.
I can't answer any of your questions on high school there but I can tell that when I went to the Nova computer shops near Taipei Main Station their prices were not (significantly) cheaper than here in Australia. Actually some stuff was more expensive.
Do you have any specific questions about living there?? Until then I'll just ramble along...
Can I assume you know some Chinese as you'll be going to school there (or are they international schools with instruction in English)? If you dont know Chinese you definitely need to learn some Mandarin and Taiwanese/Hokkien because not many people speak English (although streets and MRT stations have signs in English).
Speaking of public transport, it's 10 times more efficient and advanced than the tragic crap they subject us to here in Sydney. Buy an EasyCard and enjoy being able to get to places on schedule.
Most food is cheap and delicious including at the night markets.
Probably best not to drink the tap water. You will be within walking distance to a 7/11 from just about anywhere in Taipei and you can buy anything (including bottled water) from there.
Those buses loaded with mainlanders are everywhere, especially around the tourist traps. Arrrrr, so annoying!!! They're so disrespectful of everyone and everything.