as long as the RAID controller you are purchasing supports it, and I think it should, it sounds like what you really want is a RAID 0 + 1 array. you are basically creating 2 RAID 0 arrays, and then using the second array to mirror the first. This is still a pretty reliable setup as it would take simultaneous failures of 1 drive in each array to be unable to recover the data.
You want RAID 10 - most modern controllers support it. It would create a pair of 2TB RAID 0 arrays, and then create a RAID 1 array with the RAID 0 arrays for a total of 2 TB of fully redundant space.
I usually don't get very fancy with RAID arrays, most of the time I'm using 0, 1, or 5 in my builds. I've never used a raid 0 + 1 or a RAID 10 before, just read a little on 0 + 1 back when I first learned about RAID arrays in general. how are they different?
They are a standard RAID type, though fairly uncommon for home use (since they require at minimum a 4 disk array). They are set up just like any other RAID array (for a given controller), and should work the same as any other array once they are set up. It shouldn't be too difficult. You would not have to manually set up the RAID 0 arrays or anything - there should be an option when creating the RAID to set up a RAID 10 volume, you then select the disks you want to include, and you should be good to go. Make sure the SATA card you buy supports RAID 10 though.