This week's giveaway is in the EJB and other Java EE Technologies forum. We're giving away four copies of EJB 3 in Action and have Debu Panda, Reza Rahman, Ryan Cuprak, and Michael Remijan on-line! See this thread for details.
First book: You'll need to know some database design theory. I don't know which book to recommend here. You can search using the search phrase "Database Design".
Second book: you'll need to learn a dialect of SQL. SQL is not really standard so you should choose a database-engine to learn with. I'm using Apache Derby (also known as IBM Cloudscape and known as Sun's Java DB).
Derby/Cloudscape/JavaDB is open-source that doesn't cost anything. The SQL manual that I have is the Derby manual in PDF format which is available free from Apache.
Third book: The JDBC book that I have is Sun's definitive reference on JDBC: "JDBC API Tutorial and Reference, Third Edition (Paperback)". This book is big, but I suggest starting by reading and understanding the name of each chapter and the first paragraph in each chapter. This book is advertised by Sun as being both a tutorial and a reference. ISBN-10: 0321173848
Sun's most recent JDBC book is expensive. If you're on a tight budget, you can pickup the second editions for next-to-nothing on amazon.com.