Just like Weblog Entry I want to display custom template so user can create content page directly from there.
You need to set Insert Options on the standard values of the template for the Blog item to have a new custom template in that box.
Navigate to the Standard Values for the Blog template and click on the Assign button in the top Ribbon to add new templates.
Here's a post describing how to set this up in Sitecore pre 8, but the functionality is still exactly the same
http://www.geekhive.com/buzz/post/2015/2/how-to-configure-insert-options-in-sitecore-cms