Why I Don't Recommend Medium as Your Blogging Site
Medium has a great reader base, amazing interface to write and publish. But I would suggest not to use medium as your primary blog.
Primary blog is a space where you post your original content. The other places can have copies but the primary blog is your source of truth.
It is always a good idea to have primary blog under your name or a brand name mapping to a domain name. By adding content under this domain name you are building domain authority. When your writing gets big you get noticed
Whereas when you use sites like medium where you are just a username and not a domain name, the traffic belongs to medium and not you.
But, how to make use of medium's userbase?
The answer is cross publishing. Once you add the content to your main blog wait for 3-7 days import the blog to medium. Now it will be added as a canonical post linking to your original site.
You can also tweak the blog little bit to route the traffic to your website