Hi,
best jvm for running AS7 at the moment is still Oracle JDK6, but as Nicklas said it will be EOL soon. Current EOL time is february 2013 http://www.oracle.com/technetwork/java/eol-135779.html
JDK7 is supported with AS7 but still depends on platform are your running it might not be recommended, for instance currently jdk7 for macosx has few terrible bugs in nio impl that prevents most of communication(remoting) in as7 but can be somewhat workaround.
as for what jdk to download, use Java 7/6 SE JDK, other oracle options (EE*) are just extra download with some ee components / tools that are needed to run app server.
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tomaz