As you probably already know, these reduced forms occur in speech, not in writing (except to illustrate how to say them, of course).
"wanna" is "want to"; "gotta" is "got to", "gonna" is "going to".
I want to give my Mom something nice for her birthday.
Said: I wanna give my Mom ...
I have got to get started right now, or I'm going to be late!
Said: I've gotta get started right now, or I'm gonna be late!
By coincidence, you've chosen three forms which are accompanied by three different pronoun-verb contraction series:
"wanna" is preceded by a simple subject pronoun:
I wanna, we wanna, you wanna, they wanna. Not used for "he" or "she", and other third person singular situations: he wants to, she wants to
"gotta" is used after a pronoun contracted with "have" or "has":
I've gotta, we've gotta, you've gotta, they've gotta;
he's gotta, she's gotta
Although technically incorrect, "gotta" is often preceded by the simple subject pronoun (the same as "wanna"). I don't recommend this!
"gonna" is used after a pronoun contracted with "am", "is", or "are":
I'm gonna, we're gonna, you're gonna, they're gonna;
he's gonna, she's gonna
"gonna", but not "wanna" and "gotta", is used in the past:
we were gonna, you were gonna, they were gonna; I was gonna, he was gonna, she was gonna
Note: the 's in "he's gotta" means "has"; the 's in "he's gonna" means "is".
![Smile [:)]](/emoticons/emotion-1.gif)
CJ