In general, you're correct. Calling yourself as sensei has to be avoided, because it's an honorific word. The better word is 教師【きょうし】.
However there is an exception. If you are to become Sensei of elementary schools or kindergartens, I think it is OK to say "小学校の先生になりたい", at least informally. Kids do not understand honorific expressions, and teachers in those facilities frequently use 先生 as the first-person.
"高校/大学の先生になりたい" would be frowned upon in a formal setting.
EDIT: Actually my answer didn't mention how "高校/大学の先生になりたい" sounds like in informal situations, but in that case I totally agree with @dainichi.