since it's turn based game using swing should do. I'll briefly explain the way you use swing.... basicly you use swing components such as JPanel or JButton and override thier paintComponent(). That way you can make them look whatever you want them ... draw images, Java2D shapes, and other components in them. Actions would still be handled by mouse listener and you would change screens by drawing different components on some event.
To warn you, I never did a turn based game, only a game menu in my game
... so there could be better ways of doing turn based game.
usefull link: painting in swing