The IAA staff will help you set up a bank account through the post office, which is the default bank for government employees. Your monthly checks, other reimbursements, etc., will be deposited in that account. When opening your bank account make sure you request the capacity for online, overseas purchases with your debit card and online banking (ipost).
The post office account is VISA debit, of limited use because some vendors might not accept it, like 7-Eleven. Many people choose to open another account in one of the other banks in Taiwan in order to have the ability to have a fully functional debit/credit card. Megabank has been popular among foreigners (and have a branch on campus at NTU), but other options exist.
Citibank is a good option as well. You can open an NTD account and a foreign currency account and exchange money between them at essentially the interbank rate. If you have a Citibank account overseas, you can send money to your Taiwan foreign currency account with no fees (unsure about sending from Taiwan to the foreign country, might be a fee on the back end from the country you are sending to). Also, certain Citibank branches in Taiwan will tell you different things about setting up these accounts (e.g. "you can't do it", which is not true). Try the Xinyi branch (across the street from Eslite), as they were able to set this up. Note: this has only been tested with a US Citibank account.