We can't really give you a good a complete answer to this as the amount of data being backed up (each day) affects any recommendation (and your basic scenario probably won't work as you want anyway). Some info though.
Overwrite means: Destroy all data on tape and write new backup set at the start of the tape
Append means: Add new backup data on the end of the same tape
Overwrite Protection Period restarts it's count everytime more data is written to the tape
Append Period starts it's count when the tape is overrwritten
Unfortunately you need to rethink your strategy (and probably will need more tapes) because of the following concepts:
1) To continue adding Monday's data to the Monday tape will need a really long Append period - however you will eventually fill the tape in the middle of a backup (exact timing depending on your backup set sizes), causing the job to either be held up or fail (and /or a second Monday tape to be needed.) - Note: there is no way to only destroy the earliest backup sets on a tape to free space. At the point in time that the tape fills (assuming you have set 15 day overwrite protection), that tape will not be eligible for any kind of write operation for 15 days.
2) Similarly if you start with an empty tape or an overwrite (and allow appends), the tape will not be overwritten after 15 days, as it will contain either one or two more Monday backups that cannot be destroyed yet as they will be less than 15 days old.
3) You cannot let incremental sets be destroyed unless a new full has been run, so you cannot really do overwrite jobs unless a new full backup exists - incrementals depend on previous incrementals all the way back to and including the last full (in a chain) so delete one and you ability to restore all your data will no longer exist.
So you need to come up with a strategy that either stops appends (based on how much data will fit on a tape and what your backup sizes are) so set a shorter append period
OR where periodically your daily backup jobs start as overwrites thus resetting the append counter (and again this may need to happen based on how many daily backups will fit on a tape. Note: you can let a job use more than one tape (called spanning) but then the first tape cannot be overwritten until the second half of the first set on the second tape is no longer needed (and you have to plan for this too.)
Don't forget you will need to also be running full backups AND will almost certainly need more than 7 tapes
This may help as well:
An explanation of the "Overwrite Protection Period" and the "Append Period"
https://www.veritas.com/support/en_US/article.TECH5459
