You're right on the generation side, but that doesn't really address the hosting cost. If you pay for your own domain you can probably get the rest for free or < $1/month though.
Basically you can pick a folder in your file sharing area, map it to your domain or a subdomain of your domain, add an A record at your DNS pointing that to an IP Fastmail provides, and select whether you want it published as a website, a photo gallery, or a redirect to somewhere else.
If you are using your own domain for the website and accept the default of HTTPS Fastmail will deal with getting and deploying a certificate (from Let's Encrypt, I believe).
(BTW, you don't have to have your own domain for this. If you aren't use a custom domain with Fastmail apparently you can still publish static websites from your file hosting space. It will just be on one of the subdomains).
Fastmail accounts also include DNS hosting. If you use them for your DNS then all of this can be managed from the settings in the Fastmail client, which is convenient.