EverWeb does not have blog pages at present, but they are working on this with every update. They do have a video on their website under the Support section that shows you how to create blog pages as a workaround, whilst they fix the issue.
The best platform for you to be able to create what you want would obviously be WordPress. WordPress is designed as a blogging system and if you wanted to you could re-create your whole website using WordPress. WordPress.org has become much more advanced from when it first started out as a blogging system and it is a CMS that lots of people now use for creating websites. It is one of the easier to learn CMS's, along with Drupal and Joomla.
If you already have a web host, then use WordPress.org. Your host might even allow you to install WordPress with the one click installation, if they have it, but other than this, you can install it manually by downloading the latest version of WordPress.org from the website at http://wordpress.org and then uploading this to your server with Cyberduck or any other ftp software, such as Yummy ftp and then you need to create a database and then link the two together and you are ready to go to create your new blog and website.
If this seems too complex, then wait and see what EverWeb come up with or go to the website and have a look at their blog workaround on their support videos.