RAID 1 is optimal for redundancy. For an array of n drives, you have n-1 copies of the data, and can lose up to n-1 disks before you lose any actual data. Read performance is amazing, write performance is the same as 1 disk. Capacity is the same as 1 disk.
RAID 3 is not particularly optimal for anything. At minimum, you want to use RAID 5 (RAID 4 is RAID 3 with improved performance, and RAID 5 is RAID 4 with improved performance). RAID 5 does a little bit of everything. For an array of n drives, you have n-1 capacity, 1 copy of data (you can lose any 1 drive and still have all your data). Read performance is roughly equivalent to n-1 disks, and write performance is between 1 disk and n/2 disks.
RAID 6 is RAID 5, but with 2 parity disks, so you have 2 copies, n-2 storage, n-2 read speed, and about write speed of 1 disk.
RAID 0 provides optimal performance and capacity at the cost of redundancy. n Capacity, n read, and n write, and 1/n redundancy (if any drive dies, the whole array is gone.
For a backup system, I would recommend RAID 1, which prioritizes redundancy. I use RAID 5 for data that I can replace, but it would be a pain to, for which I need large storage capacity (read, my media fileserver). I run RAID 0 for my games - If a drive dies, I can simply reinstall games from their disks or Steam, and I want maximum performance from this disk to reduce loading times.
RAID is completely transparent, and a RAID 1 system with 2 drives is similar to your setup now, except the system would keep them perfectly in sync at all times. Any RAID array can have any number of drives, though some require certain multiples (RAID 5 needs at least 3 drives; RAID 1+0 or 0+1 needs at least 4 and must be even, and everything else needs at least 2). The entire array will show up as a single, large drive. If any drive fails within the arrays redundancy limits, then the array will continue to function fully. As soon as you replace the failed drive, it will restore the redundancy as quickly as it can copy data to the new disk; you can use the array while it is rebuilding or in this degraded state. If you lose more drives than the array can handle, then the array will fail and disappear. This would be similar to if your main 500GB hard drive and your 1TB backup drive failed at the same time.