I got the gallery working like I wanted to, using the following plugin:
https://wordpress.org/plugins/rocket-responsive-gallery/
Also, if I will have time, I will apply the information in this article:
http://ottopress.com/2011/photo-gallery-primer/
Furthermore: with this answer I no longer need the default WordPress gallery styles because I can customize the gallery myself.
https://stackoverflow.com/questions/19802157/change-wordpress-default-gallery-output