Key point for minimal blogging: It's all about your feed.
My minimal blogging tool is called Radio2. Your feed is the center of the universe for Radio2. It's used to connect to Twitter, and we hope to many other tools.
The links you push through this tool will be rendered in many different contexts. That's why the way you render it is not important. The point of the tool is to connect your linkflow with all the places you might want your links to flow. That's the reality in 2011, and any blogging tool must take this into account.
The Radio2 software can be downloaded and installed on your own server, on EC2 or Rackspace, for example, or anywhere you can run a Windows or Mac server. It's designed to be very simple to set up. I will even set up accounts for reviewers who want to get a look at it without setting up a server.
To get an idea of what it is and how it works, check out the user docs. There's not a lot of docs, because after all, it is designed to be minimal.