The Random Featured Post plugin allows you to display a random post from a designated category. Ideally this should 
draw readers landing on your homepage to some of your best posts. The featured post will display the title 
“Featured Post” (customizable) along with the post’s title, an excerpt and a link to continue to the full post.
<h3>Additional Notes</h3>
<ul>
<li>The show_featured_post($PreFeature = ”, $PostFeature = ”, $AlwaysShow = false, $categoryID = 0, $NumberOfPosts = 0) function has five optional arguments. 
The first two are for any HTML you would like to display before and after the featured post. The third argument is a 
boolean (true/false) argument which will override the \’Show Featured Post\’ option and always display the featured post when true. The fourth option allows you to 
specify a single category to display from, overriding the selections in settings page. The fifth option allows you to show more than one post at a time, overriding 
the settings page option.</li>
<li>All output is contained in a DIV class named “featuredpost” and can be adjusted via your stylesheet.</li>
</ul>

Random Featured Post

The Random Featured Post plugin allows you to display a random post from a designated category as a "featured" post.

Dekisugi

This plugin adjusts the number of posts per page of the front page based on the total number of texts in all recent posts so that its height would automatically be in proportional with the height of your widget column.

Dynamic Home Length

This plugin adjusts the number of posts per page of the front page based on the total number of texts in all recent posts so that its height would be  …

Random Featured Post vs Dynamic Home Length