First Post – Be Kind

have you tried a search:
https://www.google.co.uk/search?hl=en&safe=off&rlz=1T4SNYK_en-GBIE248IE248&q=category+icon&btnG=Search&meta=

https://www.ads-software.com/extend/plugins/category-icons/

You can use the post_class() function to apply specific classes (including those based on category name/slug) to each post.

<?php if (have_posts()) : while (have_posts()) : the_post(); ?>
<div <?php post_class() ?> id="post-<?php the_ID(); ?>">
<h2 class="post-title"><a href="<?php the_permalink() ?>"><?php the_title(); ?></a></h2>
[ ... ]

This will give you a whole stack of classes to play with such as post-150 post sticky hentry category-music tag-piano. You then use these in your CSS to apply icons to the post titles.

.post-title {padding-left:20px;}
.category-music .post-title {background:url(images/music.gif) no-repeat left center;}
.category-bikes .post-title {background:url(images/bike.gif) no-repeat left center;}