There seem to be the following versions: emacs23, emacs23-nox, e3, emacs23-lucid, and jove, as choices to download. Where can I find out what the differences are?
The short answer is that you almost certainly want
emacs23: it's the full version of Emacs 23 with graphical support.
emacs23-nox is the same, but without any graphical support. If you're installing Emacs onto a server or other environment that lacks an X window system, you should fetch this version instead. (Note that
emacs23 works just fine on the terminal, so the only reason to prefer
emacs23 is if you don't want to drag in the dependencies.)
jove are not Emacs; they're lightweight editors that have Emacs modes to them.
emacs23-lucid is XEmacs, which used to be called "Lucid Emacs".