For the layout, I would suggest that you have an outer JPanel that used something like a BorderLayout. It would contain the two end baskets and in the cetner another JPanel that employs a GridLayout to hold all of the playing baskets.
As for the classes, it looks like your Main class is superfluous - you can just put the main method in your Game class and call that. The Shared class and the Player class do not need to be represented as GUI classes, so they can remain as is. I would suggest that you have your Basket method extend JPanel and override the paintComponent() method to allow for custom painting of the beans. You have a choice with Game, you could make it extend JFrame or have it contain a JFrame.