You don't have backup needs, you have recovery needs. Backup enables you to fulfill those needs.
As has been mentioned many times above, there's no one fit answer - but I don't think you're even asking the right questions.
Under what circumstances will you be recovering data? There are two main types of recovery:
day to day recoveries where users want older versions of files or to replace a corrupt or deleted file; and
disaster recovery in case of hardware, system or site failure.
Will you support both recovery needs? If so then for day-to-day recoveries you need backups every day kept for any length of time deemed appropriate. Proper tape based backup is still the industry standard here just based on the volume. 12TB at 75% used, running full backups every week kept for 4 weeks, and daily cumulative incremental backups with 5% changes every day kept for 10 days means 51.3TB of data. Plus, you don't want all your copies on a single media, imagine if that thing failed?
For disaster recovery you need to know your RPO and RTO? Your Recovery Point Objective is basically how much data can you stand to loose while your Recovery Time Objective is how long after the disaster you can take to get back up and running. Answering these will tell you how often you need to run a backup and what storage technologies and methods are appropriate, or at least which ones are inappropriate. How are you going to protect your data from the disaster - how far away is far enough? I wouldn't consider the same campus as far enough away.
There are a number of products out there. I personally work with NetBackup from Symantec and it's pretty much an industry standard, but that's my employer's choice. I've looked at amanda (http://www.zmanda.com/) a few times, but haven't done any real testing with it. There's data protector, BackupExec and many listed at http://en.wikipedia.org/wiki/List_of_backup_software