Don't make a big applet, because it's double-buffered and will take up twice as much memory as you need.

If you're just modifying pixels, make a big PImage and use set() and get().  If you need drawing functions, you can use PGraphics but be aware that you need to use PGraphics2 / PGraphics3 / PGraphicsGL (I think) for P2D, P3D or OPENGL renderers, respectively.  Not sure about the JAVA2D renderer.  There is stuff about creating a PGraphics instance elsewhere on this board, and in the FAQ I think.  PGraphics can do everything that PImage can do, but also you can draw to it with the drawing functions. Update: PGraphics isn't working yet. Sorry!

The rule of thumb for how much memory you'll need is width*height*4bytes (divide by a million to get a megabyte count).

It can be tricky, since you need to draw everything twice to get a preview - once on your buffer and once on the actual applet.  You need to decide whether you're going to scale up onto the buffer, or scale down to preview.  Because you can't see what you're drawing onto the buffer until you've saved it, and saving and opening large images takes time, I recommend starting with a small buffer until you get it right

I think Jared sometimes uses Flash for his bigger prints, but I could be wrong.  Depending on the kind of graphics you're producing, you might have more luck writing out to Illustrator or Postscript, and rendering that to a big image in Photoshop, for instance.  I'm not sure what the status is of the AI and PS libraries though.