Whenever I start a new project, I have to do an intricate choreography to get all the pieces to complete the build. I have spares, but not a ton, so sometimes I have to move things around between 3 or 4 bikes to get the part for the new bike. If I pick up a better part at a swap meet or from the Box O' Crap, then the flow is disrupted and chaos ensues. That is also the case if I had everything laid out perfectly in my head, only to find out during the build that a particular part won't work where I wanted to use it. I suspect half of my shop time is spent going over in my head how to swap parts around in the most efficient way to gather the pieces for a build.

To answer the original question, I tend to start with the bike that needs the least work and will yield immediate results. A filthy bike or one that needs a paint job, might take a long time for me to get started.