EasyProjects.
http://www.easyprojects.net/
Not Free, Not Open Source
I've used this one and for simple to learn project management it works great. It is easy to setup and has a low learning curve for non-technical people or people with limited project management backgrounds. In addition, it can scale well for those do have this experience. It provides for quite a bit of customization, good request control and management, decent billing information, and good time and resource management features and extensive security and permission control. It would end up costing a little over $2000 out of the box for the hosted version for all 15 users and can be hosted in IIS since the entire app is browser based.
Project Engine
http://www.projectengine.nu/
I haven't used this one but I did take a look at it. Runs both as a desktop app and is accessible from a browser. The project manager can control what people need to do and they can review it from a browser. It has a simple interface and should be easy for everyone to pickup.
dotProject.net
http://www.dotproject.net/
http://docs.dotproject.net/index.php?title=Main_Page
Free, Open Source
This one is entirely web based and open source. The layout is clean and simple. This one is built using PHP and MySQL but you can download and host it yourself.
Achievo
http://www.achievo.org/product/
Free, Open Source
Documentation is sparse although there is support through the forums. It includes some interesting features such as the ability to track time spent in meetings. I have not used this in production but did evaluate it. Seemed Ok, but my biggest beef was the lack of documentation.