That's not quite accurate. There is no specific type of private key linked to each of P2PKH, P2SH and bech32, and the same private key can be used to generate an address of each of those three types.

These are all just different ways of displaying the same private key. A private key is simply a 256 bit number. The "default" way of displaying it is in hexadecimal format, which is 64 characters long. Probably the most common way you will see it displayed is in Wallet Import Format (WIF). The steps to convert from HEX to WIF can be viewed here: https://gobittest.appspot.com/PrivateKey. Essentially it involves adding a byte to the front, hashing it twice to calculate the checksum, adding the checksum to the end, and the converting it from Base16 to Base58Check. Base58Check is a special character set used in bitcoin which excludes characters which are easily confused for one another, such as 0 (zero), O (uppercase o), I (uppercase i), and l (lowercase L).

You can display the private key using any encoding system you like, such as Base10, Base64, binary, and so forth. Minikeys are slightly different, in that they have to be created first and then the full private key calculated from them by hashing them, which is a one-way process. There is no way to generate a minikey for a private key you already have.