The quick answer: In British textbooks, "to" is preferred. It's the version I hear when I speak with people from the UK. In American textbooks, "to" is only used with subordinates. In the US we prefer to use 'with' to show equality. example: "The teacher already spoke *to* the student about his poor grades and will speak *with* his parents after school."

Sorry but it's "want to" never wanna except in spoken informal speak.

I think that the difference is that if you say you want to speak "to" someone, it implies that you want to make a statement to them: you speak and they listen. On the other hand, if you say you want to speak "with" someone, you are asking to have a dialogue: We both speak and listen to each other. As a practical matter, they are used interchangeably. I also agree with the comment that it is always "want to" in written English, even if it is pronounced "wanna" in casual speech.