Startup Crontab
This simple method will simply start your TeamSpeak server instance when your server has finished booting.
Pretty much all Linux distributions support this method as crontab is installed on most distributions by default.
Add a line like the following to your crontab (run crontab -e to get to the crontab editor on your system)
@reboot /home/teamspeak/teamspeak3-server_linux-amd64/ts3server_startscript.sh restart