If you are interested in Learning Chinese, there are 4 different ways:
The teaching materials used are basically the same. The only difference is the status of your visa.
In a university program, you can apply for a student visa after four 4 months of studying. With a student visa, you will be allowed to stay in Taiwan indefinitely as long as you continue studying.
Find the Chinese programs here:
In a non-university program, you will still be able to obtain a student visa.
This is more flexible, and not formal study. your language exchange partner teaches you Chinese for free, and you teach him/her English, or another language.
If you been study Chinese before, and you feel that you can study more by your self, you can just buy a books and types, you can choose different level, from basic, middle and advanced level, study by your self will be more difficult if you only have very basic Chinese level.