MySQL would be good enough to learn as long as you're using from the command line or only using SQL commands. Many of the graphical management tools (like SQLyog and MySQL Workbench) will let you manage the database via point-and-click which doesn't really teach you anything. If you want to learn how to use the database, you will need to use SQL only. Some relevant things to master would be:
*Selecting/Updating/Deleting/Inserting data.
*Create/Alter/Drop views, procedures, functions, tables, databases.
*The various levels of normal form, specifically third normal form.
*Constraints, foreign keys, primary keys, etc.
*The different datatypes and when/why to use each.
*Managing indexes, users, partitions, replication, etc.