I have read that drives larger than 1TB are still experiencing higher than "normal" failure rates. I would therefor stick to 1TB drives. RAID-1 (that's mirroring) is safest, but should not be used as a justification not to do backups. Burn all of her irreplaceable files onto DVDs, and since even they may degrade depending on how they are stored, re-do that every year or two. You'll need four drives to create a pair of RAID-1 arrays.
Any disk can fail. If you want to protect your DATA a RAID1 would protect your DATA, but requires 2 2TB drives. If you want a single drive look at the WD2002FYPS it is a enterprise drive. It should and I say should be more reliable then the standard 2TB drive.
If the data is critical a RAID1 would be the best. It doubles the cost, but if you are not concerned about price go with a RAID1.
Even if the controller fails you can use a program like Testdisk to recover the data from a RAID.
I personally have a setup where I use a Synology NAS with 2 HDD 1TB each in RAID 1 and also I have an external 1Tb USB HDD. All my data is stored on both. The NAS allows me to access it all over the house, and the extHDD is a good backup that I can recover the data from in case the NAS goes south. Unless ALL 3 disks fail simultaneously, I can't foresee a total loss-of -data scenario.I would recommend this setup if very important data needs to be safe.