When I was an IT manager I setup a RAID1 array on a DIY Linux build for the small business I worked for. A few years in we had a hardware failure that took down the server. I don't remember the details, but we lost access to the files and everyone including me was panicking.

With all the pressure and a healthy dose of incompetence, I was struggling to wield the power of mdadm to recover the files. The bosses were in a rush so they had me send the drives to a recovery service. They were able to recover everything, even though one of the drives was toast. I think it cost the company $3,000 USD.

From that point onward, we used Synology diskstations (NAS.)

I was pretty happy with them. They had a good web UI which showed me how to set it up and would make suggestions. Mostly maintenance free; they were like little robots that did everything for me. When I was getting familiar with them, I tested yoinking a drive while it was running and replacing it with an empty drive. It started using the new drive right away and mirroring files to it. I loved how effortless it was.

We had a second Diskstation off-site, and set it up to receive nightly backups from the main office. It was another built-in feature that just worked without much fiddling.

If I were to set up a NAS today, I don't know what solution I'd go with. It's a deep rabbit hole and I'd probably have to do more research to see what works best for me. I know there is truenas which I could virtualize on proxmox. In the past I heard Linus Tech Tips praise unraid and I'd be tempted to try one of those because they look cool. And there's those cheap UGREEN NAS on Amazon and I have no idea if they're good or not. Then there's terra-master and of course Drobo which was the trendy thing for influencers back in the day...

yeah I'll stop there, but best of luck with whatever you choose!

P.S. I almost forgot-- every home should have a 45 drives Storinator 😜

How fit are you with Linux and using command line?

and a Plex server on top of that

Look into Jellyfin, it's completely FOSS as opposed to Plex, which has a little more complex business situationship

The reason I’m considering this is that, as I understand it, if one of the four hard drives in a NAS fails, I could simply buy an identical replacement drive without any issues.

Generally yes if the drives are formatted as RAID or as ZFS. The later one being my personal favorite

I’ve also thought about compressing my photos and uploading them to various sites (Terabox, Drive, MediaFire, Mega, etc.), but obviously, you never know where that data might end up.

Privacy wise this is fine if you upload encryped zip files. But I'd recommend against compression. You're going to regret compression in 10 years.

The goal is to avoid losing my photos; we have a lot of pictures and videos of the kids

Look into Immich. It's a server software which also gives a nice viewing and browsing experience

My fear is that a hard drive failure in one of our computers could cause us to lose everything.

Look into the "3-2-1" system. Having one backup is important, having a second backup offsite is even better.

I’ve been storing that sort of information on external hard drives. That way, I avoid paying for a cloud service and always have that data to hand.

Photo prism https://www.photoprism.app/ or Immich https://immich.app/ are both great self hosted options. Plex is terrible at photos IMO.