Could I always use "have" (and never use "have got")?

English is not my native language. I have constantly been trying to add as more words as possible to my active vocabulary. But there are words which I understand but don't try to use myself. One of them is "have got" instead of just plain "have".

I always use "have".

Is it a good way of learning and using English. Or am I missing something?

"Have got" is used when you possess something or when you must do something.

• I have got ten dollars. (I possess ten dollars.)
• I have got to go. (I must go.)

It can't be used in place of have in all cases. On the other hand, have can be used in any place where we use "have got".

• I have ten dollars.
• I have to go.

Neither of these sound strange or formal/informal. So, your strategy of only using have is a good one.

(Of course, there is also "have got(ten)", which is the present perfect tense form of the verb get. In US English, there is a difference between "have got" (as above) and "have gotten" (past perfect), while in British English, both are generally "have got".)

There are at least three different phrases here, with different usage patterns

"I have [got] to" = "I must" : in British usage, "got" is usual, and omitting it is rather formal. I think this is less true in N.America

"I have got", the perfect of "I get", in different senses (eg "get" = "obtain", "get to" = "reach"). "Got" obviously cannot be omitted. Americans often prefer "gotten" in this sense, but until recently this was unknown in the UK.

"I have [got]" = "I possess". "Got" is normal in colloquial UK English, but is, or used to be, frowned on by prescriptive teachers. It is particularly common in the negative and interrogative ("Have you got?", "I haven't got"), I believe for prosodic reasons: Americans say "Do you have?" and "I don't have", but until quite recently these were not used in the UK except in a habitual sense; so the alternative "Have you?" wouldn't take the forceful stress pattern of "have you got?" I don't know how common this use is in N. America.