You will probably be best off if you invest in a proven solution.
Tapes are definitely not the way to go, for your size a disk based solution would be better and much easier to maintain.
When you are on the TB scale, you should consider using something with compression and deduplication. In a solution like this you will only store unique data that is common on several copmuters ,and have references to these unique files or blocks.
You should also make sure that whatever your backup server starts with, the product supports expandable storage. So you can start with 10TB, and add on more disks as you go.
With several computers an agentless backup client would also be favorable. So that you can backup your whole LAN from a single backup client. Some products also include a virtual computer based on an FTP/SFTP/FTPS location. So you could have your backup client on windows and backup all the LAN machines + the linux machine from the same interface.
I wouldn't use an approach based on either of 1) Incremental backups and 2) differential backups. With incremental backups, you will want to do another full backup eventually, or at restore time you'll have to restore too many backups. With differential backups, you will want to do another full backup eventually, or eventually your differential backup will get too big. In your case you would have to re-send the 10TB. That is not acceptable.
Make sure when you seed the data to your backup server, that the data will NEVER need a new re-transfer if it is not changed.
Make sure that you don't NEED to restore full backups, and that you can restore only a subset of what you backed up and that you can select from backups as they were on the day you are restoring from.
Backing up data should be allowed from offsite locations, and even if the backup client is offline. In the case that they are offline there should be a 'large initial backup' option for later importing at the server.
Be sure to chose a solution that has built in MS SQL backups and exchange backups, and that you don't need to re-transfer everything each time you back them up. It should support hot backups of these items.
An example of a product at this scale that supports all of the above is ROBOBAK. (I also work for this company)