I use OpenJDK a fair bit on some systems and it's pretty good as it has the encryption libraries we need etc (unlike GCJ). The Oracle JDK is a bit faster as it's JIT engine is pretty good, but has been working out ok for me personally.
So I think we're saying we recommend Oracle's JRE as that is the one that we do most of our testing with, but OpenJDK should also work fine.
In terms of version - just pick the newest stable one you can (i.e. Java 7) so you get all the latest security patches etc.