Since you want to be application developer who understands a DBMS.
In my opinion there exists, five foremost databases in minds of developers. These are
- SQL Server
- My SQL
Why these five, first three because of market share. Last two because of usage share in open source applications.
Also you stated that you are working with JavaEE.
Then I suggest you choose one of the following. In the following order.
- PostgreSQL Open Source
- DB2 (Universal) Express Edition
- Oracle Express Edition
- SQL Server Express Edition
I put SQL Server last since you are working with Java. Other databases are more appropriate. Note that I am Certified in SQL Server (2000,2005,2008). Therefore this is not a bias in my opinion but I acknowledge that others are more strong with Java.
I put MySQL in last rows since I believe you should start with a DBMS which supports SQL Standard more, and first three are better (out of box) than MySQL in this regard.
There are not much difference for learning application development with first three. If you are to be primarily open source developer choose PostgreSQL. If you are to be primarily commercial developer, look your local career site. Which DBMS wanted more, choose it. For example Oracle is more popular in my local area.