Okay. I need some gpg advice so this doesn't happen again.

I have some webspace on a server and so I had this wonderful, brilliant idea! I was going to gpg encrypt 3 folders on my own computer, then use FileZilla to upload them and store them on my server. Since they were encrypted, it should be good. Kinda like my own private DropBox with unlimited space.

I automated this and did this little procedure once a day and all was good in lala land until the dreaded time came....

I wanted to reinstall Linux (I was bored) and I thought, No problem! My backups are installed safe and sound on my web server site. I'll just redownload them later with FileZilla and unencrypt them!

Well everything went marvelously as planned. I reinstalled my Fedora 27 KDE. I reinstalled FileZilla. I downloaded my encrypted folders from my site... except when it came to the small pesky problem of dencrypting my own pgp folders. At which point I was told I could not. The exact error message was:
What is the correct way to do this so it doesn't happen to me again? I'm assuming it's because I didn't have a backup of my public and private keys. Is that correct?

I bet this is not a problem with cryptography.
Have you checked the rights on the file that you try to decrypt?

Secondly. When you install Linux and want to overwrite an existing system, it helps to have the home directory and possibly all other files which are not needed for the system to function, on separate hard disk partitions. That is what partitioning is all about.

Installing an operating system does never mean to lose your private data, documents, collections.., whatever. On the other hand, when you prefer to keep these data on an external drive, on a remote server (as gentle hosting-services or malicious weasels are eager to provide) or other, then why keep a local copy? At least, you would immediately stumble over any problem with the encryption, should there be one.

There is none, I bet.

The good news is, I think: file open error probably means exactly what it says. Check permissions and triple-check your command line. If the key was missing or wrong, GPG would tell you that, not this.

I keep my most critical cipher keys on non-volatile media such as CD-ROMs as well as memory sticks which are kept locked in a fire-safe.

... I forgot one more thing, yesterday.

If you use encryption to protect files that only you will access to, afterwards, let's say in exactly the way that the OP described, above (for example), symmetric encryption is most appropriate. All the same, you may choose a key-file in this case and might run into trouble when you lose it.

But even if you content with a nicely composed passphrase, symmetric encryption (option -c to gnupg) is alright in most cases, where you do not need to communicate data to other people.

(There had been a short exchange on LQ where someone stated and wanted to impose the contrary. But I am right and she/he was wrong. Foll Stop. Look it up in case of doubt. It is in the book right beside the Grimms' tales and a better read, anyway. Believe me.).

I'm a gpg noob myself, so take what I say with a grain of salt.

"file open error" -- this may just be an issue of file permissions. I will point out that, when decrypting files, you should generally specify an output file name or GPG will simply dump the decrypted output to your terminal window. You might consider this command:
It's my understanding that gpg would search for the appropriate key in your gpg key ring. If you failed to back up this key, you are s.o.l.. If you made a backup of the keys, you'll need to import them (at the very least your private key) to your key ring before trying to decrypt anything that was originally encrypted with them.