Macbook Air and a Mac Mini

Good morning folks. I have what I hope is a simple question: What's the best and most affordable way to connect with my Mac Mini?

I have a 2006 Mac Mini and a new MacBook Air and would like to be able to configure my Mac Mini so that I can use it's screen sharing features. The issue I am having is that I no longer have a display nor do I have a USB keyboard, which would allow me to put the Mac Mini in target disk mode. I'm thinking that I can get a thunderbolt converter that will allow me to use my MacBook Air as a display but is there another option that I might be overlooking? Any thoughts and/or tips/tricks?

Thanks in advance!