It turned out to be as simple as:

sudo apt-get remove --purge mysql-server mysql-client mysql-common

sudo apt-get autoremove

sudo apt-get autoclean

sudo apt-get install mariadb-server

This won't break your phpmyadmin, or any webapp, as long as you say no, when asked if you want to delete your database and you use the same credentials you used for you mysql-DB. Also back up your data before doing this.