How to change post appearance depending on their category?

you could try and use the post_class() in your post div, which would give you a lot of additional css classes to style your post with.
(explained here: https://codex.www.ads-software.com/Migrating_Plugins_and_Themes_to_2.7
https://justagirlintheworld.com/take-advantage-of-the-new-sticky-post-feature-in-wordpress-27/ )

or you could add the category slug in the folowing way (assuming that the post has only one category) to the post div; something like so:
<div id="post-<?php the_ID(); ?>" class="post <?php $categories = wp_get_post_categories(get_the_ID()); echo get_category($categories[0])->slug; ?>">

and then style your special post in ‘mini’ categeory like so:
.post.category-mini { ... } in the first case; or
.post.category-mini { ... } in the second case.

Yeah, I think post_class() is what I was looking for. I’m not sure I’ll be able to implement this (I’m not exactly a programmer), but I’ll try.

Thank you, alchymyth.