My suggestiong is using scene2d for menu or HUD stuff. Check this out : https://github.com/libgdx/libgdx/wiki/Scene2d
scene2d is a 2D scene graph for building applications and UIs using a hierarchy of actors:
- buttons
- labels
- sliders
- text buttons
- scrollable views (lists)
- tables
- your custom widgets
- group of actors
You can add ClickListener to an actor. (In your case the actor is a Button)