I would say that your backup plan is sort of odd. You absolute need to run T-log backups when you have full backups, yes. Differential backups on the other hand, maybe, but not an absolute must.
To set up a backup plan, you first need to have a restore plan. That is, if there is a disaster, what are your RPO and your RTO?
- RPO - Recovery Point Objects - how much data can you lose? The last 15 mintues? The last minute? Nothing at all?
- RTO - Recovery Time Objectvie - How long downtime can you accept? One hour? The full day?
These are questions that your business may have to answer. When you give them the costs, the may backtrack on their original requirements.
When there is a disaster, the normal procedure is:
- Restore the most recent clean full backup. (If there has been corruption going on in the system, that may be not be your very most recent backup.)
- Restore the most recent differential backup taken after that full backup - if you have one.
- Apply transaction log backups taken since the last differential.
If you are taking daily full backups, I don't see the point in differentials. I think differentials are useful if you have a database that is large, so you only want to run a full backup on weekends, and then take daily differentials so that you don't have to apply t-log backups all through the day. But the exact tuning, of this you can only find out by testing the restore operation to verify that you meet your RTO.
How often to take T-log backups depend on your RPO, but I would say every 15 minutes is good bet.