Dragboxes in a page (Dashboard kind of display which is clickable)
I would check into jQuery UI/Drag &amp; Drop.
http://jqueryui.com/demos/ 

After you get the hang of this, create a template file for your homepage.
Create blocks with different content and render them in your homepage template file.
Apply the drag and drop interface to the blocks you rendered on your homepage.

This is just a quick look on your question, but it should get you in the right direction.