First of all, you have to know why your drive failed. No need trying to resuscitate it if it will die "again" in a few months

Of the choices you propose :
1/ The safest way it to backup on an external drive (in case your RAID card dies, you have a completely separate backup).
2/ If the external HD enclosure is not reliable, then connect the drive to the motherboard (and not to the RAID card). Thus, if the RAID card dies, you still have a backup on a different system).
3/ The least reliable system would be the RAID 5 option as you do not have ANY backup.
All this being said, this discussion doesn't take into account the basic rule of backup: put at least 10 km between the source and the backup and you need at least 2 copies of backups. In your configuration, if your computer burns or is stolen or ..., then the data
and the backup vanishes.
Of course, it all depends on the value of the data. If it is just some music or films that you can D/L (oups, what a nasty thing to do

), then no need to be a "crazy backuper" and your system will be ok. If the data is the pictures of the family over a 20 years span, then you need to be a "crazy backuper"

Robby