If want to ensure the integrity of a backup, would it be a necessity to use a checksum on all of my backups and not just the 'verify backup' option?
CHECKSUM Specifies that the backup operation will verify each page for checksum and torn page, if enabled and available, and generate a checksum for the entire backup. This is the default behavior for a compressed backup.
All the verify backup option does is confirm that the header of your backup is readable, nothing else.
Neither of these options will tell you that you have a good backup! The only way to confirm that your backup is good is to restore it on another system