What's the best type of car?
Sorry, depends on your requirements. There are some extremely light databases like Hypersonic (HSQLDB) but while it is fine playing around it isn't suitable for real systems. MySQL is a good free database with a rich set of features but is harder to set up and maintain. Something large scale like Oracle is so rich you can make a career of learning what it can do, but you run the risk of learning Oracle rather than JDBC.
Helpful?
Dave