The reason why I usually suggest PostgreSQL before MySQL is because MySQL is far from the standards (SQL-wise). It does not support the use of window functions (8.4 version), common table expressions (8.4), CHECK constraints, EXCEPT/MINUS operator, even FULL OUTER JOINs... Even though you may have never heard of these words, you'll have to use those concepts at some point.
I strongly suggest you to start with PostgreSQL, then you can learn what "real" SQL is. Then, you can decide if MySQL is sufficient or not.
P.S. I started with MySQL and I regretted it. I now use PostgreSQL and I love it.
