Hey, I have two Medium blogs that point to my custom domain. They didn't charge me any money, and in fact the Support guy went above and beyond to help me the issues I was having with my domain name provider. But, I see now they are charging $75 for it and I'm a bit taken back.
If all you need is a blog, might I suggest Tumblr? They (as long as I remember) don't charge you a thing. You won't get an SSL certificate though.