I hate to say, but the Onegai Teacher manga was a huge disappointment. Unlike most cases, the manga was based on the original anime and in my opinion they did not do a very good job on the adaptation. Many elements of the anime are missing (for example the character of Hatusho has practically no part in the manga) and there were significant changes in the storyline, all of which made the whole thing weaker.
My advice is to just stick with the anime, and give the manga a pass.