I would suggest looking at freenas also. One thing though, is that it is suggested to have 1gb or more memory for every tb of disk space you plan to use on it. I am in process of building a nas using freenas. So far I like it a lot. You can utilize zfs, and use redundancy with software raids (so you don't need expensive raid controllers).
I would highly doubt a pi would hold up and do what you want. I've had both the 256 mb and 512 mb model. I've put 3 different os's on, and the thing can barely power a wireless keyboard dongle. I've gone through like 6 different power sources trying to find one that will be optimal, but no change. If I view system load while doing some of the most basic things (like opening a browser), it wraps out pretty quickly. I would not rely on a pi for backing up my stuff, but i'm also interested to see if anyone else has done that with a pi.
Hope that helps!
FYI, Amazon has a really good deal on a nice nas box (amazon deal of the day).
and Newegg has a killer deal on some 3tb drives right now:
So good day to do it I guess! 160 dollars off raid box, and about 30 dollars off each drive you get.