Full Disk Encryption with Time Machine Backup
You can enable FileVault 2 from System Preferences > Security &amp; Privacy > FileVault.  Just press "Turn on FileVault..." and full disk encryption will be setup. 

Full Disk Encryption in this sense means that all your own data on the Macintosh HD file system will be encrypted. There is a preboot partition that isn't encrypted, as this is where the software necessary to decrypt the drive is stored. Without it, you wouldn't be able to boot the Mac.

When you plugin the USB drive, macOS will ask you if you want to use it for backups. If you confirm that, it will ask you whether or not you want the backups encrypted. Set the checkmark and encryption of the backup will automatically be setup for you.

If you have already started backing up to the external disk without encryption, you can enable encryption afterwards like this:

Open System Preferences > Time Machine. Click "Select Disk..." and remove the external disk.

Do it again and select the disk again, and it will ask again for encryption. Set the checkmark and you'll be asked to set a password. The disk will then be encrypted. The backups already stored on the drive will be preserved.