I found Ghost while looking for a new blog engine for my company. My first instinct was to use Medium as well, but I ended up hitting a lot of issues because it was impossible for us to customize it (add custom javascript, charts, disable the lame "highlights", custom domain was not free, etc...).
1. Ghost is open source, developed by a foundation in the open. They make their revenue open, their issue tracker, their code, everything.
2. Ghost is self-hostable, as well as hosted on a paid plan. The paid plan is a little pricy (https://ghost.org/pricing/) but I recommend it if this is for a company blog.
3. Ghost is beautiful out of the box. Here is the default theme: https://blog.ghost.org -- Here is a slightly customized theme: https://articles.hsreplay.net
4. Ghost has an excellent featureset. It's powered by Markdown and has a wonderful markdown editor in its admin/authorship interface. It also supports authors, editors, contributors, drafts, publishing schedules, tags, etc.
Seriously, try it out. I'm not affiliated, just a huge fan. I want to see more people use and support these fantastic open source tools, rather than complain about Medium like there's no alternative.