If you are receiving update reminders you presumably have a Java version already installed. Go here;
http://www.javatester.org/ and click on the 'Test the version of java your browser is using' box. A pink box should appear giving details of your version, mine reads 'Java Version: 1.6.0_14 from Sun Microsystems Inc' which is the latest one. It is correct that most Java updates are for security reasons.
If your current version is older that Update 14, you need to uninstall all old versions and then get JRE Version 6 Update 14 from the link posted by 1002richards or from here;
http://www.java.com/en/download/manual.jsp
PS. You should probably opt for the 'Offline' version of the download for Windows (15.50 MB).