TPE is the airport code for Chiang Kai Shek International Airport in Taoyuan. Are you asking how to get from the airport to Taipe City?
If so, then the cheapest would be Kuo Kuang Airport bus that drops you off at Taipei Main Station. Cost NT$120. Other buses like E-GO, Airbus etc will cost you NT$140 but will drop you off at various hotels in the city.
Limos from the airport to any destination in Taipei City will run around NT$1300+. I think the last time I heard, they’ve raised it to NT$1800 
And welcome 