So you are proposing 2 menus, one without buttons as an intro, and another with the button?
The two most common ways are:
Using an introductory movie: you export your AE intro as a video with the audio. You create a timeline for it. The end action of the timeline is the main menu with its buttons.
Using a loop point in a motion menu.
Since you do not appear to want any motion in your menu, I would use the introductory movie. It can look like your menu, but I see no need to add it to a menu.
I will render the intro in After Effects as an AVI file so I can include the music.
There is no reason to export from AE only to have Encore transcode it. If you use the introductory video method, just export it from AE as MPEG2-DVD. Encore really prefers the separate files (m2v and wav or a3c); there is no sync issue unless something is done wrong.