I love the sound of a double bass. They are very harmonically complex. In the hands of a good jazz bass player, they can do some amazing things.

Here's a couple links to sites on how to build your own acoustic and electric upright basses. I think the electric could be one of the simplest lutherie projects you could do, and very rewarding as well. Such a simple body and neck, plus no frets would get you a very playable instrument for not much time invested.