I went with the prepaid FarEastTone card for a couple of months before I got my ARC. I don’t even remember whether or not I had to show my passport to get one. You can buy them at 7Eleven. for registering a new number, they are 1000 NTD including 300 NTD worth of air time. Afterwards, you just buy the airtime. It also seemed I got a free number of SMS with each new purchase of a prepaid card.
I switched to post-paid as soon as I had my company licence. I went to their office on Tunhua, and the girl who took care of me seemed very professional (unlike other businesses like my bank where every time I feel like the very first foreigner to change money in Taiwan because nobody knows how to deal with it). Anyway, she filled out the form for me, asked all the right questions and offered on her own account to copy my phone book from the old SIM card to the new one (I kept my number but got a new SIM card).
They are in fact the local representative of AT&T. I never bothered to compare cell phone contracts of different companies, I preferred to stick with FarEastTone because they seem professional enough and it is very convenient to have English menue. Roaming always worked after I got the post-paid account (but HK was VERY expensive), and I can send SMS to my most important relatives and friends in Germany because they happen to be with the German provider that has a contract with FarEastTone (or possibly AT&T).
But I think a couple of other companies also offer these prepaid cards that you can get at 7Eleven, like Chunghwa etc. So maybe it would make sense to compare prices. Does anybody happen to have done that?