Most often, this type of situation would call for something called a DMZ, or demilitarization zone. In a nutshell, this would mean keeping your internal servers internal behind a firewall limiting any outside connection. On the other side of the firewall would be any publicly accessed web servers etc… which should also be behind some sort of security appliance. This in effect, creates a sandbox where you will be able to very much control access to sensitive data while at the same time keeping availability at it’s necessary levels.