Which Java package should I use: OpenJDK or Oracle JDK?

OpenJDK is the default version of Java that Ubuntu uses and is the easiest to install while Oracle Java 7 is Oracle's own version of Java 7.

You can read Ubuntu Java Documentation.

OpenJDK: "Oracle makes the OpenJDK source code available under an open-source licensing model. It's both gratis, and free (as in freedom) software."

Further as I found in Oracle Java FAQ Section

For Oracle JDK

"The Java Development Kit (JDK) is free to download and use for commercial programming, but not to re-distribute."