There are lots of ways to do this.
I have to agree that RAID alone isn't the most safe solution; RAID + backup is better. I think there are a some things you need to decide, the main one being whether you need to back up everything
you have. With a NAS we are talking several terabytes and chances are all of it isn't irreplaceable. For example, downloaded movies can likely be downloaded again. While losing your collection would suck bigtime, this is stuff that can be replaced at the cost of some time and perhaps money, while your own photos can not be replaced if they are lost. Think about that and see if you can segment out what you actually need to back up.
If you decide that is all or a significant volume of data, one of the most practical options would be a NAS box that has an eSATA port and some kind of incremental backup function in its firmware/OS, coupled with an eSATA cradle similar to this
and a few large capacity bare drives.
That will get you the lowest cost per megabyte and the full hard drive performance you need to back up lots of data. Bare drives should be handled with some care (reuse the antistatic bags when storing them), but are durable enough. We keep decades of data archived on bare drives at work.
As a side note, if you can't find a good fit for your needs in a store-bought NAS, remember it's just a tiny computer with a capacity for some number of hard drives. There are various hardware choices out there to build your own and you can have it running a general purpose operating system (Windows, Linux), or any of the several NAS OSes out there that aim for the appliance-like feel of the store-bought devices. I built a Windows Server machine using the HP MicroServer
for myself, but there are many more choices out there.