i always advise to use have / don't have because it's okay to use in any cases. have got has a narrower and more specific meaning.
Both "I haven't got" and "I don't have" are correct. Just make sure to use them properly. For example:
- I haven't got a clue that he was cheating on me.
- I don't have a clue that he was cheating on me.
The following lesson on verb tenses might help you: