New to Java

I'm relatively new to Java and I'm working on making a standard, simple game. Now I've looked through the Java Applet tutorials and I can make basic Applets that show graphics and whatnot. But I am interested in making an executable version of this run by a Driver Class. I'm not able to make the paint(Graphics g) function return say, a BufferedImage, and I'm not sure how to make an instance of the applet and use it like a frame - for example Frame frame = new Frame("blah") and then set the graphics to that via Graphics g = frame.getGraphics();

I'm also curious what other people think in terms of what is best for a game. I have heard Applets are good, but there are of course the Frame options and so forth. I actually had an easier time with JFrame, but it was skipping and such(I know there's a way around that, I just didn't get around to implementing it). I would like to get the Applet working better, however.

Any advice would be helpful, thank you.

- Bob