It seems that a lot of the time when you word 'got' is used, it's unnecessary, e.g. "I have got a/ I have a". Is there any rule as to when the word 'got' should be used?
Most such structures are informal ones originally used in American English. I should start worrying about it, Miss Z, only if you hear Brits beginning to use their past participle 'gotten'!
My goodness...that was quick, Miss Z! Just an additional point. We started using these mainly because of our tendency to elide structures such as 'I have' into 'I've'. 'Got' was handy in order to avoid sillinesses such as 'I've it' instead of 'I have it.'
'Gotten' may be American now but it used to be English - same as 'forgotten' still is. They're consistent, we're not (not that consistency ever has much to do with the use of language).
Virtually the only time 'gotten' is used in modern British English usage is in the phrase 'ill-gotten gains'. As Jno's answer suggests, however, 'gotten' predated 'got' by about two centuries.