A "customer database" (or a Customer Relations Management system aka CRM) is used to track and report on interactions with customers... not employees.
It sounds to me like you are looking for something to track and report on employees... is that correct?
And an operating system is a platform/interface used to work with the computer and execute programs. It's a little more bottom line that what you seem to be looking for (kind of like saying that you know you need to put oil in your car so you're wondering what kind of engine to buy).
What you are looking for is an application or program that you can use to manage the employees of this business (from what I can gather, at least).
I did a quick search and found this:
ManagerAssistant|Employee Performance Management Software, Employee Performance Appraisal, Employee Performance Evaluation, HRweb, HR Web
I'm not endorsing that program and no nothing about how good it may or may not be... but that might get you started in the right direction.
Or you can build an intranet, as Kia mentioned. It would be somewhat the same thing but customized... and has the potential for much more.
EDIT: Ok, just realized that Kia is also who originally ASKED the question lol