China Airlines is not too bad. Well, they once forgot to properly close a door of a Boeing 747 - but not much happened.
In general, they are good and cheap. New airplanes (mostly A330 on Asian routes). I went to Jakarta with them last week. Total price including all taxes, fees, surcharges and whatsoever: HK$ 1200. For nearly 5 hours of flight time it's a pretty good deal.
Back to the topic: Thai Airways also flies to Taipei and is quite cheap. Unfortunately, their website sucks for international flight bookings. Contact a travel agent instead or check Your Online Travel Agency - Cheap Travel Deals - Zuji - Hong Kong 你的網上旅遊大師 - Zuji 香港.