Categories overview that links to page displaying posts

There is no need to create a custom taxonomy or custom template.

When we click on any category then wordpress by default called archive.php file which has code for display posts related to that particular category.

So first use this code in any of your php template file to display category lists:

<?php
$args = array(
  'orderby' => 'name',
  'order' => 'ASC'
);
echo '<ul>';
$categories = get_categories($args);
foreach($categories as $category) { 
    echo '<li><a href="' . get_category_link( $category->term_id ) . '" title="' . $category->name . '" ' . '>' . $category->name.'</a></li>';
} 
echo '</ul>';
?>

Which display category titles, likewise you also can display category descriptions and images.

And when you click on the category title, then it will call wordpress archive.php file which display posts related to that particular categoty.