Category Lists on a Page

I’m trying to find a plugin that will allow me to choose a category and display a list of its child categories on a page.

In my specific example, I have a category called ‘projects’. Each of it’s child categories is the name of a project. Each of those project categories contains posts about that particular project.

So on my ‘projects’ page, I want to display the page text as an introduction followed by the list of projects. Clicking on a project will take the user to a category archive of posts about that project.

Can anyone suggest a plugin that will allow me to do this? Failing that, is there a way to code this into a theme template?

Thanks ??