"I want to study in a normal university" The sentence structure is correct. The grammar is correct. There are no typographical errors. However people may wonder what a "normal university" is. This is one of those rare cases where we have some English words, which are commonly used in China, but aren't actually commonly used in English speaking countries. For example, if I do an internet search for "normal university", 99% of the results are for universities in China and Taiwan. Many English speaking people from other countries may misunderstand your sentence and think that you wish to attend a "typical" university, or a "common" university - synonyms for "normal". Despite the potential for misunderstandings and confusion, I would have to say that I still consider the sentence to be completely correct.

"Normal" is not a common description for a university or for most institutions. I can't offer suggestions because I'm also unclear as to what exactly you're trying to say here, lol. As a general statement, I would say something like: - "I want to study in a university because I want to be a teacher." - "I want to go to university so that I can become a teacher."