Fact of the matter is this: RAID will keep you from losing everything based on the problem you had, but if you write bad data, you will be writing bad data to multiple drives. As to the RAID config, going RAID1 is the easiest to implement but you lose half your storage. It is also transferrable since were you to lose your mainboard and a drive, you could pull one of the drives and drop it in another system and not worry about the RAID config - RAID1 doesn't shape your data storage to fit - once you get into striping (5, 10) then you'll need to concern yourself with the platform.
As to backups, keep in mind that your backups shouldn't be running when you are, so scheduling the backups for late night / early morning (for the normal person) is a must. As such, network speeds are less important.
Should you so choose, you could back up to local drive(s) in a similar configuration. The only reason to go NAS is if you're trying to prevent something like a severe power spike (think lightning) from killing your entire system (including the drives).
I'd suggest doing a monthly or at least quarterly backup of all your critical data - OS's and software can be recovered. I would also suggest that you have at least one copy on optical media and stored in a dark, dry place outside the reach of sunlight and extreme temperatures. It is more effort, but is cheaper and then you KNOW that data isn't subject to the whims of electrical currents. You may want to periodically read the disks to make sure they still work.