Many bloggers display their category list on the “Home” page to provide a good navigation to the viewer. If you want to arrange the list in an order per your choice then download the “My Category Order” plugin and show-off the category from your blog in your way.
Simple way to include the list of category is by using the below mentioned piece of code where you can see that the list would be in an order of “Name of Category”.
<?php wp_list_categories('orderby=name&include=3,5,9,16'); ?>
Once you will activate the “My Category Order” plugin in your blog and will replace the above piece of code with the below mentioned one, then you can arrange the list as per your choice.
<?php wp_list_categories('orderby=order&include=3,5,9,16'); ?>
To define the order of category, you will have to enter in the “My Category Order” window from your wordpress dashboard. There you will get the full list of your defined category where you can drag each of them to arrange in your way. To show a particular category at the start position, just place that category at the top and then arrange the rest in similar manner.
You can see the demo on the “Header” part of this blog where the list of category is shown in a customized fashion (Not in an ascending or descending order).