It is written in many places how these things are. But what not easy to decide when to use which of them, as it needs a deeper understanding to choose.

So I want to note the quick heuristic methods to choose these.

Public vs. External

TL;DR;

So if you know the function you create only allows for external calls, go for external. It provides performance benefits and you will save on gas.

Basically, public means it can be external or internal, the compiler need additional work for the public function. With the external only, it allows arguments to be read directly from calldata, saving the copying step.

Easy read here:

• https://gus-tavo-guim.medium.com/public-vs-external-functions-in-solidity-b46bcf0ba3ac
• https://ethereum.stackexchange.com/a/19391/76945

Memory vs. Calldata vs. Storage

TL;DR;

• use calldata when you only need read-only data, avoiding the cost of allocating memory or storage.
• use memory if you want your argument to be mutable.
• use storage if your argument will already exist in storage, to prevent copying something into storage over into memory unnecessarily.

Ref:

• Easy example on why storage over memory

To research more

I am still not sure why most of the OpenZeppelin libs choose to use memory over calldata, although they don't mutate them. For example: https://github.com/OpenZeppelin/openzeppelin-contracts/blob/master/contracts/token/ERC721/ERC721.sol#L179