RAID1 is the best solution for your needs, I think. With any decent RAID1 system, both HDD's contain exactly the same info at all times. If one HDD fails, the system immediately reverts to the mode in which the remaining good unit is the only drive in use, and it keeps on working. It also puts out a message on the screen telling you that a failure of the RAID1 system has happened, so you know a repair is needed.
There are two "weak points" in this, but easily addressable.
1. On some RAID1 systems, the failure message may show up as a window on the main screen. BUT an untrained user may find that box just annoying without recognizing its importance, and just close it. So it is possible for you as the system manager to not know the problem happened. It would be very useful to get into the habit of checking the RAID system for error messages. In my case, the simple way I do that is to reboot from time to time and watch the start-up screen messages for the RAID system report.
2. When you get the failure report, you need to get a new replacement HDD unit and then schedule some downtime for repairs. Ideally this will be within a few days, although the remaining good HDD might well keep functioning for years. The RAID management system should help you identify which HDD unit has failed so you know which to replace, and then it will rebuild the array by copying all data from good old unit to new unit. Although often this rebuild can be done as a background activity while normal operations are going on, I prefer to let it happen with no "normal operations" to slow it down. But that's a preference, not a need. So you DO need some downtime to replace the failed unit and rebuild the array - as much as several hours if you have an array with a terabyte or two of data and you want the rebuild to proceed by itself. BUT the point is you can SCHEDULE that downtime. Until you do, the computer just keeps on working with no interruption.
As others have said, RAID1 is NOT a backup system at all, so you need to set that up additionally.
A CAUTION. There is no standard for any RAID system. Thus, if you have a RAID array of any type operating and the RAID controller system fails (either a mobo's built-in RAID, or an add-on controller card), it can be difficult for a new controller to read and use the old HDD's. There ARE ways to prevent this problem, starting, of course, with regular backups. But to try to ensure that a new controller can deal with old HDD's:
1. If you buy a dedicated RAID controller card, get one from a well-established manufacturer that is very likely to still be there in 10 years or whenever you might need to replace that card. It is very likely they will still have cards in their product line able to deal with your HDD's correctly.
2. If you plan to use the RAID system built into the BIOS of the mobo, do what I did. I surveyed the makers of the common mobo chips - the Southbridge - used to control the hard drives.On a mobo it is this chip and its associated controller code in the BIOS chip that provide RAID management. At least one maker (nVidia in my case) offered an assurance that it will continue to use the same RAID algorithms in its future chips so that their future products on future mobos will be fully able to handle HDD's written by their earlier chips. So I chose a mobo using such a chipset. I actually had to use that assurance a few years later when the mobo's voltage regulator section failed. I chose a replacement from a different mobo manufacturer that DID use a chipset from that original company (nVidia) and, when it was installed, the system booted up completely normally. I did not have to make ANY adjustments in the RAID system! So, look for chipset makers that offer such an assurance, and choose your mobo accordingly.
3. Last resort, I would consider, is that there are software packages out there that claim to be able to read any old RAID set of HDD's and recover your data for you if your old controller failed. I have no experience with these, and am not completely comfortable with that. However, I do recognize this: among the several types of RAID, all quite different, RAID1 is the simplest because each HDD unit contains ALL the data written in the same form as any "normal" stand-alone HDD. It may have some uncommon info in the Partition Table and/or Directory structures that make is not quite trivial for an OS like Windows to read only ONE HDD from a RAID1 array, but I'm pretty sure most data recovery software would be able to get around that easily.