Given that you are just looking to test fiestaware you may want to consider a spinthariscope rather than jury rigging your own geiger counter. They don't need batteries, and provide a visual indication of radioactivity. And they meet one other of your requirements--they are cheap.
I saw a resistor in the schematic that was labeled 4700k. Does this 4700k ohms? By the way, I found some radioactive fiesta-ware today. I also have a video about the fiesta-ware I found today, if anyone is interested.