You can travel easily using the Taipei Metro to most of the tourist attractions and destinations. This should not be an issue if you come from a country with mass rapid train services. Connecting on a Metro is more easy than a central or connecting train station.
I have used the Taoyuan Express to travel from the airport to the Taipei Main Station. It is best that you can get your hotel or AirBnb within walking distance of the MRT Station.
This is one of the best travelling card that you must have in Taipei. It allowed you to travel on the Metro, local trains, express train from Taoyuan airport and many others. It save you time queuing to purchase single trip tickets and money for the trips. There is a deposit of NT$100 for the card. You may keep the card and use it when you are back at Taiwan in future.
Please remember to have a data roam plan or purchase a local data SIM Card. You will need it to access Google Map or Apple Map. They are the best companion on DIY trip. I use Singtel ReadyRoam services and my family will share the local data SIM Card purchase from Klook so that we can stay connected when we get separated in the busy shopping district or night markets. You can also opt to purchase at the Taoyuan Airport or at retailers in Taiwan.