'gotta' is informal, mostly verbal and national and generation specific. People in their 30-40's, particularly Americans, seem to accept it more than others. For me, seeing it written, in anything other than song lyrics and quotations of conversations, where the point is make the pronunciation explicit, is garish.

"I have to say" and "I've got to say" both mean the same thing. In the first sentence, we are using the verb "have" and in the second, we are using "have got". "I gotta" is an informal contraction of "I (have) got to". I hope that helps!