Como usar Have/Has got e Have?

Quando começei a aprender ingles, fiquei um tempo confuso para entender a relação entre as sentenças com have/has got ou apenas have/has.

Ex.: I’ve got a great idea / I have a great idea. [Ou seja, que forma eu devo usar?]

Basicamente, podemos dizer que os dois tem a mesma ideia de posse. Portanto, nesse sentido, tanto faz dizer I’ve got a nice plan ou I have a nice plan.

Veja como é o uso com os outros pronomes.

I have a very funny nickname = I've got a very funny nickname.
You have a very funny nickname = You've got a very funny nickname.
He has a very funny nickname = He's got a very funny nickname.
She has a very funny nickname = She's got a very funny nickname.
It has a very funny nickname = It's got a very funny nickname.
We have a very funny nickname = We've got a very funny nickname.
You have a very funny nickname = You've got a very funny nickname.
They have a very funny nickname = They've got a very funny nickname.

Ou então, algums vezes, é comum ouvir os nativos falarem have/has got to contraído pela forma gotta.

I gotta a very funny nickname
You gotta a very funny nickname
He gotta a very funny nickname
She gotta a very funny nickname
It gotta a very funny nickname
We gotta a very funny nickname
You gotta a very funny nickname
They gotta a very funny nickname

O mesmo ocorre quando queremos usar para algo que você TEM que fazer.

I have to work = I gotta work.

O mesmo ocorre com todos os pronomes pessoais.