Yep, the world of Java can be quite overwhelming at first, and sadly the Oracle website doesn't help much to alleviate this, in my opinion.
If you want to start developing with Java, all you'll need to download is a JDK, which you can find here.
Unless you have a specific goal in mind, like a certification for a specific Java version, I'd go with the latest Java SE 7 JDK, which is currently called Java SE 7u5 over at the Oracle download page (at the top). This includes everything you need to get started.
Also, you may want to stop by our JavaBeginnersFaq (<- click). Among other things it includes a section (18. What is a JVM? JRE? JDK? J2SDK?) that attempts to explain the difference between some common - but confusing - acronyms like JVM, JRE and JDK.
Build a man a fire, and he'll be warm for a day. Set a man on fire, and he'll be warm for the rest of his life.