Buying train tickets in advance

I'm coming to Taipei this Friday and I've decided I'd like to head straight to Hualien. So my plan (thanks to wix99!) is to take a bus to Taipei Station from the airport, and then catch an express train to Hualien.
However, I'm assuming on a Friday late afternoon/early evening, all of those trains will probably be full, so I'd prefer to book my ticket in advance. I've been going through the website (http://railway.hinet.net/), and it looks like I can make a reservation, but I have to go and pay for the ticket at a train station before the date of departure. That's not possible because I won't be in the country until the date of departure. Does that mean that I can't actually purchase a ticket until I get there?
Is anyone aware of a way around this, or do I just have to roll the dice and show up and hope I can get a ticket?

Thanks again, guys,

Jason

I was able to book online here: http://www.railway.gov.tw/en/index/index.aspx

I didn't use a Taiwan credit card; I think you might have to use IE.

Hey drumbrake, were you actually able to purchase tickets from that site, or just reserve them? I went to the link you gave, and then chose "Internet ticketing" and it just took me to the site in my original post. I'm unable to find where I can actually purchase tickets, not only reserve them.
The problem is that I want a ticket for the Friday, but I don't arrive in Taiwan until Friday. The site says that if you reserve tickets, you have to pick them up no later than the day before departure.

Thanks

I was able to purchase the tickets online for Taiwan railways (not the HSR). I then collected the tickets from the main railway station in Taipei. I'm in Mainland China now so unfortunately cannot access the site, but I think it was in Chinese - so you might need the help of a Chinese speaker to help you navigate the site. I'm pretty sure I reserved the tickets, and then used the reservation number on the online booking page.

the site is bilingual, and you can book the tickets and pay online, and get the real ticket just before departure from a special counter (internet booking).