I’d only build your own if you’re already extremely fluent in elixir/phoenix (ie. it’s dead easy for you), or if you want to do so as a programming exercise in its own right. If your primary motivation is to write, then use something off-the-shelf. Unless you have some specific reason to need something more dynamic, I’d start with a static site generator. Hosting is free or cheap, and maintenance/security a relative non-issue.

There’s not much point in recommending a particular SSG - any recommendation is only going to reflect personal taste. All the known ones work and are more than sufficient for a personal blog. Think about what facilities you want and whether or not you’ll need to do any deep customisation (in which case choose an SSG written in a programming language you already know). Then pick two or three matching your criteria from (eg.) Static Site Generators - Top Open Source SSGs | Jamstack, make a quick choice, and start writing!

If the author would decide to write it’s own blog then a blog post from Dashbit website would be an amazing source of inspiration:

GitLab Pages https://docs.gitlab.com/ee/user/project/pages + some static site gererator (Hugo in my case https://gohugo.io/)