My dream would be a Stroh bass. There are only a handful left in the world, and I doubt one will ever come my way, let alone at a price I'd want to pay. The Stroh range of stringed instruments was developed for the early recording age, the idea being that the horns gave a directional sound and were thus easier to mike up.
This is the bass, pictured below. I've actually seen such a beast, in an antique shop on Kilburn High Road many years ago, but never played one. God knows what they sounded like, but boy do they look cool.