I believe in Taiwan people use traditional Chinese characters for writing whereas in China they use simplified characters. Assuming this information is correct I'd like to kindly request suggestions for good textbooks teaching Chinese using traditional characters. Thanks a lot for your help.
Learning the characters is mostly a matter of memorization. You will need to learn a lot of characters in the most efficient way possible. Textbooks are not good for this. Using a spaced repetition system is normally the best method. A free spaced repetition program is Anki (http://ankisrs.net). You can find "decks" of traditional characters within Anki to start learning.
A pay version of Anki that lets you write the characters stroke by stroke is Skritter. I personally like Skritter and have been using it for several years. I find writing out the character helps me to remember it.
To supplement the learning of characters you are going to want to get some form of grammar textbook. I like Ross's "Modern Mandarin Chinese Grammar."