Is USB-C to USB-C the preferred transfer method now?
It appears the most important thing when using any backup from a previous iPhone is having your Apple Account password. If you don't know it but are logged into Apple device(s), you can initiate a password reset. And maybe even if you aren't currently logged in, the security landscape changes daily if you haven't noticed.
If you don't have space in iCloud for a full iCloud backup, Apple has provided temporary space for an iCloud backup to transfer to your new iPhone. There will be a "get ready for your new iPhone" under iPhone>Settings at some point, and it will offer the space there.
I think the iCloud Restore started via Quick Start is probably the fastest and easiest method. And most people don't like transfers between devices as they lock you out of both devices until the process is complete. With iCloud Restore it will complete most of the transfer and then let you use the phone while it continues to download apps, email and messages, settings, and files.
Apple support document regarding setting up a new phone:
https://support.apple.com/en-us/102659
It includes articles about using iCloud Restore or wireless transfer between phones.
Another article that includes restore from backup from iCloud and from Encrypted Backup on Mac.
https://support.apple.com/en-us/118105
Here is a wired transfer document:
https://support.apple.com/en-us/117383?device-type=iphone
Good luck and may the force be with you. lol