I do not know if any of my answer satisfies your question.
AFAIK, in every bitcoin address format there is an equivalent format of bitcoin private key. I only have a prior knowledge with regards to this but I think I am able to share it with you, so please bear with me.
These are the 3 types of bitcoin address format in the mainnet.
1. Segwit compatible (P2SH) - P2SH stands for (Pay 2 Script Hash) that starts with 3.
2. Legacy Address (P2PKH) - (Pay 2 Public Key Hash) begins with 1.
3. Segwit Native(Bech32) - that starts with bc1.
These 3 addresses differ from different private keys.
I don't have any any idea about the derivation from the type of private key to create a bitcoin address.
bitaddress.org supports 4 private key formats:
base-16 or hexadecimal which is the encoding of the number (without any addition) in base-16
base-64 same as base-16 but with a different character set
base-58 which is special encoding used in bitcoin with a checksum
minikeys which is a special short format of private keys used in some collectibles (physical bitcoins)
you should use compressed base-58 as it is supported by all wallets so it can be imported in all of them.
Is this the same with
Private Key WIF (WIF),
Private Key Hexadecimal Format (HEX),
Private Key (B64),
Mini?