There's nothing wrong with a single HDD in an old desktop except for the risk of failure.

I would start by getting one hdd that's the same size or larger than the one you have and using it as backup. If the old HDD is very old and small you can probably find a larger one cheap, don't go out of your way to find another small and old one.

Something like Borg Backup will be perfect if you use a Linux filesystem because Borg is incremental, has deduplication and compression built-in. There is a very simple graphical app for it called Pika Backup (for Linux).

There are other solutions if you use Windows but even a simple copy of your important files is better than nothing. Get a HDD and copy files to it right away.

Another backup solution is to buy a DVD or BluRay burner (can be USB or internal) and backup super important files to optical disks. This may or may not be cheaper than a HDD.

Do NOT rush into RAID, Unraid, TrueNAS and other fancy stuff like that. Your priority right now should be backup not RAID. RAID is a convenience for keeping a system running when a HDD fails but it is NOT a replacement for a good incremental backup.

After you have a backup in place and use it regularly you can consider whether RAID and availability is something you want/need.