There are several hosts that will let you host. I prefer Github Pages because of the simplicity of Jekyll and that it uses Git and plus you get free Github CDN and a nice github subdomain.
Otherwise self-hosted Wordpress or Anchor Cms is the best option.
Hosted Wordpress does not give you much flexibility, typically. Medium seems to intentionally enforce a style consistent with other blogs on the service. Tumblr's editing tools can be annoying sometimes but in my experiences it has been the most customizable.
I think it's worth it to host yourself, but if that isn't an option and you want flexibility then I'd go with Tumblr.
