I should think that the best way is to use server-side technologies
(JSP, servlets, etc) rather than an applet. Or possibly a combination of
the two.

Even if Access was a server database (it's not - it's file-based) it
would almost certainly be a Bad Idea to open it up to the public
internet for just any bugger to attack your server. Keep everything on
the server and only allow HTTP access, and you don't have that problem.

BTW, Access is a distinctly suboptimal solution for this type of work.
You'd do well to explore some of the better free DBMSs such as MySQL or
PostgreSQL (which has a native Windows installer as of the latest release).

Luke