Typically, your init process will be a shell script of some sort that sets up your environment (launches daemons, mounts partitions, etc.) and then launches your app. There are several "slim" environments (SLiM login manager, Slim for PHP5, Slim templates for Ruby, etc.), so I'm not sure which one you are referring to. If you need an X server, launch it from the shell script you have as your init process and then launch your app from with the init process shell script or as some start-up script in your X environment. As long as the init process shell script launches all of the pieces that you need to get everything working, and the shell script never terminates, you'll be fine.
Andrew