In Vector, boot scripts are in /etc/rc.d. If you installed apache and MySQL from Slack/Vector packages then there might be a rc.apache or rc.mysql script in /etc/rc.d. Make them executable:
chmod +x /etc/rc.d/rc.apache
and they'll start when you reboot. If you don't see a rc.apache or rc.mysql script, then add the commands to start them to /etc/rc.d/rc.local. Then they'll start at boot.