what charger do I need for an iPhone 12 Pro Max? Lightening? USB-C?

This is the cable that should come with your iPhone 12 Pro Max.

It will not come with a charger/adapter. But this information should be helpful:

Power adapters for iPhone - Apple Support

At the time of writing this (February 2023)* you need a connecting lead that terminates in a lightning connector to fit the port of your iPhone. The connector on the other end of the lead will need to plug in to the charger and this will depend on which type of socket is on your particular charger, though typically it would be a USB A (full-size connector) or a USB C (smaller connector). Some chargers have a captive (built-in) lead with a connector moulded on the end, in which case, you will need one that terminates in a lightning connector (again, at the time of writing: February 2023)*. The Apple 20W charger with fold-away pins is recommended, with which you would need a USB C to lightning lead.

[Edited by Moderator]