How should I backup my new MAC?

Welcome to the Apple Support Communities.

To back up, you need an external hard drive. Here’s a few excellent ones sold by Apple: 

• LaCie Mobile Drive 4TB External Hard Drive USB-C - Apple
• LaCie 4TB Rugged USB-C Portable Hard Drive - Apple

You can then follow the steps in this Apple Support article to setup your Time Machine backup: Back up your Mac with Time Machine - Apple Support. 

Also, moving forward, I recommend that you use iCloud in addition to Time Machine to sync all your files and photos to all your Apple devices. Although iCloud is not a "true" backup service, iCloud can also act as an emergency off-site backup, but this is why iCloud should be used in addition to Time Machine. Here are some resources on setting up iCloud for Mac:

• Upgrade to iCloud+ - Apple Support
• Set up iCloud Drive - Apple Support
• Add your Desktop and Documents files to iCloud Drive - Apple Support
• Set up and use iCloud Photos - Apple Support

After you setup iCloud, turn off "Optimize Mac Storage" in System Preferences > Apple ID/iCloud. That way, all changes made to files in iCloud are also backed up to Time Machine. If you have this setting on due to a limited amount of storage on your Mac, that is fine. Just know changes won't be backed up to Time Machine, only iCloud.

Jack

• Enable iCloud storage for photos etc.
• Attach an external USB drive (twice the capacity of your boot drive) for the sole use of Time Machine
• Use an app such as Carbon Copy Cloner to backup onto a separate external USB drive which can be stored off site.

This will provide three levels of "back up"