I’m hosting my sites in NearlyFreeSpeech.NET.
It’s a DIY webhost for experienced webmasters, running on FreeBSD servers, and offering full SSH and SFTP access. Paid support is optional, but they do have an extensive FAQ and a members forum.
It’s a great option if you’re writing controversial content (and so worth the learning curve), since their only restriction is that everything you do should be legal.
Another reason why you might want to consider them is their model: Pay as you go (prepaid) in terms of resources used, and they charge by the penny, so you can deposit as little as $2 dollars. The base cost for a production site is $0.05/day. Extra charges depends on how active/popular your site is and on the additional features you use, like DNS and email forwarding. They also give you the choice of server for each site: PHP/CGI, Static, Custom, and Generic.
Another reason is enhanced security. Because they host controversial content, they are used to attacks on their members’ website, and so they have strong security measures in place. But the downside of this is that they restrictive files and directories permissions, and they disapprove (and maybe prevent) installing/upgrading CMSs using the web interface. They do have a custom control panel, but most administrative tasks (like plugin updates) are done using SSH and SFTP.
In regards to installing ClassicPress, they have detailed instructions on how to install and initially setup WordPress, and you can easily adapt that. For other CMSs, you’re on your own.