Creating a new website for a friend

This may be hard to understand from the title, but I would basically like to create a widget that lets you create a list (ordered or unordered) of links. I’m making this for someone so it should be easy to use. They don’t understand anchor tags and such. And so when they would like to add a link to the list they can just click “Add new link” and they enter text to display and then the hyperlink. What would be the best way to go about doing that? In a nutshell, I guess I’m just asking if there is an easy way to add in a couple of widgets designed by me.

UPDATE: Is there a way to disable all of wordpress’s default widgets? I know I can delete the default-widgets.php but if I update wordpress won’t those files come back?