You can't move server_linux.sh there, the script expects the server binary to be in the same directory. What you can do, however, is make a small shell script that cd's into the directory of server_linux.sh and launches it. That should be simple enough.
Please do not run the server as root (or anything else that does not require it.) In your init.d script, you can use su to launch server_linux.sh as a different user.
EDIT: For your info, you might want to look into this: Debian's start-stop-daemon can launch daemons as other users. Also, it might be interesting to launch server_linux.sh inside a GNU screen or tmux session, because it spawns an interactive admin console which is more convenient to use than rcon (and also shows the game log live). Then you can just resume the screen session from ssh and see what's happening on your server or issue server commands directly in it. If you're running a server that needs good supervision, I suggest having a look at rcon2irc too, it's an administration tool that relays server events to an irc channel and, if you know Perl, you can code modules for it.