Matthew Butterick with probably the most astute and complete takedown of Medium as a platform for your writing I have read:
In truth, Medium’s main product is not a publishing platform, but the promotion of a publishing platform. This promotion brings readers and writers onto the site. This, in turn, generates the usage data that’s valuable to advertisers. Boiled down, Medium is simply marketing in the service of more marketing. It is not a “place for ideas.” It is a place for advertisers. It is, therefore, utterly superfluous.
“But what about all the writing on Medium?” The measure of superfluity is not the writing on Medium. Rather, it’s what Medium adds to the writing. Recall the question from above: how does Medium improve the Internet? I haven’t seen a single story on Medium that couldn’t exist equally well elsewhere. Nor evidence that Medium’s editing and publishing tools are a manifest improvement over what you can do with other tools.
If you use it, I would personally urge you to leave Medium and take control of your writing. WordPress is easy-to-use, easy to set up, and you can put together a basic site on a host for around $100 a year or so. (If you want to give this a shot, for most beginners I usually recommend DreamHost.)
Or if you don’t want to worry about hosting and all that stuff, come host your site on WordPress.com. You own your content, you can take it with you if you leave for a self-hosted WordPress installation, and it’s backed by world-class support. (I work there; I know these people and they are the finest.)
(h/t to Matt for the link)