It's a question of formality.
"I have" is neutral English - fine for any situation, including the most formal contexts.
"I've got" is slightly more informal - fine for most situations, including informal writing, but not for formal contexts.
"I got" is colloquial speech. This is very informal, and it is advisable for you to avoid using it.
[NB It is of course fine to use "I got" as a past simple form of get - as in "I went to the store and got (obtained) some milk this morning"]