How can I restrict a user's ability to modify settings or install apps? Our team is planning to buy around 10 Android phones for the team members. We don't want them to install any applications other than the ones provided. Is there a method or an application which would allow me to restrict the ability of a user to install apps?

As an analogy, on Windows the admin can configure the system so that other users cannot access Internet settings, task manager, or install new software. We'd basically like to do something similar to that.

One idea I had was to download the Android source code itself and then program it according to my needs and install it on the devices. However, I would prefer to avoid doing that, if possible.
You can't... unless you manufacture the device by yourself.

You can't stop power users from flashing ROM which would flush your software based protection (even if you have embedded the solution in ROM to survive factory reset). Unfortunately, almost all devices in Market support it. If not, there are ways to hack bootloaders, too.

If you are still interested in software based solution, try contacting Soti. They provide such type of solutions at a cost.