I would never use a phone mount on a bike. Even a cycle computer is overkill for a beginner. And always, always keep your phone in a plastic sealed back (Ziplock bags work well) in you pocket (on a cycling shirt) or in your bike bag (under the saddle, etc). Sweat, rain, puddles, etc conspire to eat your phone faster than you eat lunch. Mounting a phone on the bars will just distract you, and you cannot operate it without stoping anyway.
gloves, helmet, glasses.
small pump, tire levers, 3 allen keys, mini pack of pre-glued patches, one spare tube.
water bottle carrier and bottle (but you can just buy bottles of juice with a cycling-style spout from 7-11 ).
floor pump, with metal barrel and dial indicator.
shorts and jersey. Bib-shorts are much more comfortable on long rides. Assos are too expensive: Castelli, Champion Systems, Pearl Izumi , Sugoi are cheaper and just as good.
A good bright rain jacket if you want to ride mountains in winter.
Lights only if you commute late. Don't plan on riding home late through the city unless you're experienced. and those pissy little lights won't make you much more visible in Taipei's traffic anyway.
a lock, although they're overrated, especially for more than ten minutes. The New York rule is that bike plus lock must equal forty pounds: a forty pound bike needs no lock, while a ten pound bike needs a thirty pound lock.
And just never a stand, or an umbrella holder, or a flag.