Phil,
Let's not get caught up in the nomenclature of my policy names. That is how I identify my policies and the way you've currently named yours is perfectly fine. It's great that we are hashing this out, because this gives me time to ensure that our backup policies are working as expected. I am not a BE expert so please test and re-test anything I've suggested to ensure that your data can be restored properly.
First, policies are a way to group your common backup jobs to have greater control over them using template rules. For instance, we have payroll data which is high availability data in our corporation. I have a policy that controls both the back-up to disk and back-up to tape media. That data is first backed up to disk and then the policy duplicates the job and backs up the data to tape. Then I have a template rule that states when the back to disk is complete start the back-up to tape. This is just one example of what you can do with policies. Restoring from a disk based back-up is a lot faster than tape. Again high availability data.
Another less complicated policy that I use is Differentials to tape Mon - Thurs and Full backup on Fri. Again, one policy groups two templates that are required for this job. One template would be for "Daily Backup" and the other "Weekly Backup". I am forced to have two templates because each backup type has different parameters.
Now that I have a better understanding of your backup needs, this is what I would do in your scenario. However, in the end you will have four total backup jobs. 2 for Linux (Monday and Tues-Fri) and 2 for Windows (Monday and Tues-Fri). There is no way around this given how you've already defined your back-up structure.
The only thing I would change in what you've outlined is to consolidate both Linux Media Daily and Linux Media Weekly. Create one policy named "Linux Media" and then define your templates as "Daily Backup" and "Weekly Backup". Then set your parameters within each template, e.g. "Linux 5am so Linux runs on a Tuesday & appends to media". Those jobs will run according to your schedule. Do the same for the Windows Media Daily and Windows Media Weekly.
So now your job setup should look something like this.
Backup Selection List:All Linux Servers
All Windows Servers
Policies:Linux Media
>>Define one template as Daily Backup (Set parameters like schedules, day, times, append, etc)
>>Define a second template as Weekly Backup (Set parameters like schedules, day, times, append, etc)
Windows Media
>>Define one template as Daily Backup (Set parameters like schedules, day, times, append, etc)
>>Define a second template as Weekly Backup (Set parameters like schedules, day, times, append, etc)
Then you create new jobs by applying each selection list to its corresponding policy name.
>>All Linux Servers -> Linux Media = Two scheduled jobs
>>All Windows Servers -> Windows Media = Two scheduled jobs
I hope this helps.