Self signed is better and more trustworthy. LE’s short cert expiration makes it an enormous pain in the ass. Just put your cert on your site and sign it.
Even if you obtain the self-signed cert out of band (and explicitly trust it), how do you authenticate that channel?
Self-signed certs are not scalable or particularly useful for internet users. Please don't recommend this.
If your 'lets encrypt' cert is not renewing on a chron job or something you are doing it wrong.
Every guide I've seen involves setting this up.