Static variables are saved as long as the browser stays open.  You need to
explicitly reset static variables if you want them reset.  Similarly, the
saved information can be useful in other situations.

static or instance variables?

What do you mean by "quit the applet"?  There is no defined way to quit
an applet.  An applet has no way of expressing a desire to be "quit."  
If you leave a page that has an applet on it, the normal thing thing
that will occur is that stop() will be called, and then start() will be
called when you return to that page.  This prevents a bunch of shutdowns
and startups of the VM in a single web site.  destroy() is called at
some unspecified time if the browser wants to shut down the applet, but
there is no way for an applet to specifically request that the browser
do that.

Ultimately, you are responsible for performing any initialization in
start() and stop(), or providing the user an explicit means of resetting
the applet to its original state (for example, and button or menu item).