If you want to move on to Java EE, I recommend you learn about a particular DB, then how java connects to it. Next is Java beans, then app servers.
For learning, get a free or “free” DB. Download the J2EE SDK and try writing apps that use the DB.
Next, find some common things you’d use across different apps and make beans that implement.
Finally, you should look into app severs. I’m a fan of JBoss – but I’ve not used many of the others such as websphere.
With that in mind, you can look up the relavent books on Google.