You could use applets for the user interface of the game. But you said the database part of the game is very important, so I would put the parts of the application which work with the database on the server. And having made that decision, I would then probably not bother to write an applet to interface with the server. Unless there was some reason to have complex processing at the client side, I would just write a regular web application with an HTML interface.
Don't let your opinion of JSF deter you from learning about web applications. JSF isn't the only way to write a web app; that would be like me saying "I heard that Norway is expensive so I don't want to go to Europe".