Some good questions you have FS-180!
I would suggest arriving 1 week prior to finalise your accommodation and gain a bearing of your local surrounds before commencing your Chinese studies. Believe it or not, some students actually arrive the day they are scheduled to commence their studies, so giving yourself 1 week should be fine. The idea is to have already planned and booked your accommodation prior to your arrival. Arriving 1 week prior will give you a type of insurance in case the accommodation isn't quite what you expected.
Have some backup to in case you don't like what you see. A good idea is to also get the place to email you a
photo of the accommodation. The less suprises the better.
Some good accommodation links for Taiwan:
As you will be studying Chinese, we don't offer an airport pickup service. However, getting to Taichung or Taipei is quite straight forward.
CKS International Airport, Taipei provideds luxury buses from the airport to Taichung City. Buses leave every 15 minutes and the bus trip takes 2 to 2.5 hours. It costs around US$6.
Hope the above info helps. Let me know if you have any further questions.