new page template and widgets

Hello, I’m new to wordpress and building my first site with it. I come from an MS .NET background and I’m digging wordpress.

Ok, now, here is what I’m trying to do. I downloaded a free theme that has a few widgets and a basic page layout, now I want to create a new page layout with new widgets for this particular page and remove the predefined widgets on the page such as search.

Here is an example:
I have the home page it has all of the widgets needed
I want to create a department page that has widgets only pertaining to the department such as IT. So I want to add IT widgets only. I want to do the same for other departments. use the same page template but widgets for that department. I want every page unique, how can I accomplish this in WordPress since there is no real page to edit or modify?