When generating a certificate what would more secure - generating a self-signed certificate using PGP or using a public CA like Let's Encrypt? We are using it for signing and encrypting.
What are the advantages and disadvantages?
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I would advise you a third way: use a private CA. A true public CA is a complex thing because in order to be trusted you must publish your policies and have your root CA accepted by major browsers.
But for local use, a tool like xca allows to easily manage a bunch of client or server certificates, and trusting them all is just a matter of importing the root (private) CA.
Nothing is really hard here (I successfully created and used dozens of certificates that way), but you have to know the basics about X509 certificates.