Do not go medium. My advice would be to not go to any hosted blog service at all, actually. I know it’s more of a learning curve with self hosted but you get all the flexibility you want with that and won’t be tied to any vagaries of third party services (like Medium changing their platform over and over again and being all naggy now. No one likes that.) But this depends on how technically savvy you are and how much you’re willing to pay (honestly, a $5 digital ocean droplet is enough for most).
The benefits of this might not be apparent initially, and honestly when starting off the biggest blocker is the actual writing rather than any admin stuff, so do that first, and do it anywhere, as long as the platform lets you have control over the domain, and you can export everything.