Quick start or restore from backup?

If you have a Mac or a PC with itunes installed then you can take backups easily and economically before trying a transfer . Backing up the computer seals the deal.

All the methods below will transfer the contents of the phone reliably.

See the instructions in:  Transfer data from your previous iOS device to your new iPhone, iPad, or iPod touch - Apple Support

All three methods preserve and restore all data. No data is lost in any of the three methods.

Quickstart is not a restore method, it is a method to transfer all your data from an old iPhone to a newly activated iPhone

iCloud backup and restore obviously requires a lot of storage and a lot of time.

Note:

A backup from your a computer doesn't include:

• Content from the iTunes and App Stores, or PDFs downloaded directly to Apple Books
• Content synced from iTunes, like imported MP3s or CDs, videos, books, and photos
• Data already stored in iCloud, like iCloud Photos, iMessages, and text (SMS) and multimedia (MMS) messages
• Face ID or Touch ID settings
• Apple Pay information and settings
• Apple Mail data
• Activity, Health, and Keychain data (to back up this content, you'll need to use Encrypted Backup in iTunes.)

iCloud backup doesn’t include information that is synced and stored in iCloud, like Contacts, Calendars, Bookmarks, Mail, Notes, Voice Memos, Messages*, shared photos, iCloud Photos*, Health data, call history, and files you store in iCloud Drive.

*-If you had turned on Messages in iCloud & iCloud Photos, your content is automatically stored in iCloud. 

Your words have changed from the original post

1st you asked: which method yields the cleanest restore

Next you asked: nothing gets left out

Hence please refer to my earlier two posts.