1st time to Taiwan and I'm confused with the different types of trains available.

May I know if I'm travelling from Taipei to Hualien for 1 day then move on to Wulai for another day before moving back to Taipei for 6 days then move on to Alisan for 1 day and back to Taipei again.

What type of travel pass should I get? I loved trains and would like to seize every opportunity to hop onto to a train.

So far, I've only managed to get a MRT train ticket from the airport to Taipei main station, and I'm lost thereafter. Would really appreciate some advice here.

Thank you