RAID 1 gets you redundancy which provides improved uptime (keeps working in the case of a disk failure and allows you to replace the disk), but you're right to say this isn't a backup so kudos there. You can live without the data for a week, so buying new disks and restoring from backup wouldn't be a problem. So for this reason RAID 1 doesn't give you much advantage, but it is nice to have it keep working with no full restore from backup required. I'm planning to use RAID 1 for my home NAS as well partly for this reason - plus terabytes are pretty cheap now. I guess it is up to you to determine if it's overkill or not.
RAID 1 also usually gets you better read performance, and is particularly better parallel usage like txtechhelp described. I agree that the network speed may be a bottleneck in throughput so the improvement might not be noticed. I would use the spec listed by the NAS manufacturer - particularly because hard drives generally don't transfer data at their specific SATA potential rate (though some SSDs do). However, access time/latency can also be improved with RAID 1, not just throughput, so that's something you might notice as you open files.
For offsite backup, a basic suggestion would be to use an external drive that is at least as large as your primary storage, then leave it in a safe place normally, but periodically bring it home and run a set backup software schedule that covers all your data. Once backup is finished, store it back at the off-site location. The only cost is that of the drive initially, no recurring cloud subscription fee. Depending on the amount of data the tradeoff can play out different ways but you can do the calculation. I don't use cloud for backup yet because the storage space for the money isn't quite there for me.
Here is an article from StorageReview.com with some nice graphs for a WD VelociRaptor 600GB single, RAID 0, and RAID 1, and for different real-life scenarios such as file server, workstation, HTPC, database, etc., pretty interesting. One graph there actually shows better write throughput as well in 4K random writes.