Hi,
first of all you need a static ip of wich the FQDN can refer. You could also try this with some dynamic dns services, but this is sometimes very tricky. (Try DynDNS or No-IP etc.)
At some cheap Hosters a domain name is less then 1€ the month, think about it ;-)
In the next step you need an official cert for the given FQDN, this can be reached with the free of charge service from Let's Encrypt.
regards,
Tom