Info about Train service around Taiwan
(No point trying to book online, as you will need to collect sometime before travel. Go there and get the tickets is easier. But the train schedule page is good for planning) (Shedule) (Online Booking, give it a try, and u will understand) (Ticket Price info)

High Speed Rail, they call it 高铁
(Half the time, twice the price and comfort. Gd to try) (Everything is here, schedule, price, and phone-booking)
Alishan Forest Railway, 阿里山森林铁路
(Slow, limited space, but a muz-try scenic ride for tourists) (Schedule)
(Ticket Booking... But muz collect 7 days in advance.)
Tainan City Bus Service Guide.
(Fast and efficient way to get around the city.
Brought us to various historical sites.)

Taipei Rapid Transit.
(Just like our MRT, best way around Taipei City)