You’ll want to make your animations in After Effects, export them as AVI or MOV, and then use them as your video background for each menu.
Then you link each button in your starting menu to each menu that you want to play. You then set each button to Auto Activate (check this in Button properties). This will cause the button to activate when you select it, which will take you to the animated menu.
Then in your animated menus, link your buttons to your timelines/chapters.