Just a tip for the OP -- quite a bit of good info on this kind of topic has already accumulated in existing threads, so you might want to browse through those, too. You can run the Searchfunction, input either 'bread' or 'cheese', select view by 'topic', and choose the 'Food' forum, and you'll get the best results, including threads with these titles:
Fresh Western Style Bread for sale
Where can I buy good bread in Taipei?
WCIF decent bread in Gongguan, Taipei?
Fresh bread in Carrefour
Where to find good cheese?
and so on.
BTW, if you want to save money, go to Costco first. They have good ciabatta and bulk cheeses at good prices. Carrefour also has good, affordable breads. If you can pay gourmet prices, go to Jason's in B1 of 101, or Breeze Super or the one in the Far Eastern basement, and you'll get better selections.