If you want to travel from Taipei Main Station to Taoyuan Airport, your best option is by far taking the MRT (metro / subway system).
The MRT ride from Taipei Main Station to Taoyuan International Airport only takes 35 minutes. This is much faster than taking the bus or a taxi. The bus might be cheaper, but you will probably get stuck in traffic, especially if you travel during the week.
I only recommend taking the taxi if you need the convenience of door-to-door transport, or if you are carrying heavy luggage. Taxis can take forever during rush-hour and holidays. Uber is another option, but as of 2020, they are the exact same price as taxis. Zero doubt about it – taking the MRT to travel between Taipei Main Station and Taoyuan International Airport is the option that makes the most sense, both economically, and in term of travel time.
How much does it cost to travel from Taipei to Taoyuan Airport by MRT?
The fare for a single journey trip from Taipei Main Station in central Taipei to the airport in Taoyuan by metro is 160NT$. The trip takes about 35minutes.