If you plan on going outside of Taipei there are a lot of buses and trains. The trains are slower and cheaper and the railway network includes the western, eastern northern and southern lines.
The island-wide railway network, including the western line, the eastern line, the north link line, and the south link line, provides convenient travel in a number of train classes: economy, Fu-Hsing, Chu-Kuang and Tze-Chiang. Travels can choose the class of train they want according to their schedule and budget. small narrow-gauge trains operate on (mainly tourist) branch lines: Alishan, Jiji, Pingxi, and Neiwan. These trains give visitors a chance to see the caried scenery of Taiwan close-up as they travel around the island.
It is especially difficult to get the train tickets during long holiday periods, so reserving tickets 14 days before departure, by phone or by website, is strongly recommended.
ADD: No. 3, Beiping W. Rd., Zhongzheng(Jhongjheng) District, Taipei City