The most basic thing that you need before preparing for a trip, of course you must do some research. Unless you follow tour then its a different story. You would need to decide what kind of trip you wants to go for. For example; shopping, sightseeing, food eating, etc.
For this trip of mine the focus would be the culture, some local stuff, food, sightseeing, etc. Of course a little shopping is a must. Since this is a winter season, it is critical that you take care of your body. Although Taiwan does not snow, but it often rains and have heavy winds. Uses lotion, lip balm, moisturizers, apply some mask, wearing the appropriate outfit to cover every part of your body from head to toe to make sure that you are warm. You might want to bring umbrella or raincoat. But no worries you can get it anywhere there conveniently.