[Blas]

The water level in your chrome expansion tank should be up to the divider inside the tank. Remove the cap (when cold) and stick your finger inside the tank, you will feel the hole in the baffle plate. Any extra coolant will be sent to your overflow tank (assuming you have one)
Smith’s gauges work or they don't. Accuracy is another story. The standard SPF temp gauges use capillary tubes.
A wildly reading gauge says you have just air in the intake manifold. (You hit steam then coolant hence the wild readings) You can try purging the system by opening the expansion tank (NOT when engine is hot) Start the engine, add fluid to expansion tank. The water temp sensor is usually in the front of the engine, look for a small brass tube wound with a steel wire. Loosen the brass fitting on the end of this brass tube and watch for air escaping along with a little coolant. When the air is gone you'll only get coolant. Tighten it back up. Having the front of the car higher than the back helps too when doing this.
Did you have the small hole(s) on your thermostat disk orientated up? If there are none on the thermostat disk, you can drill one. Careful with the thermostat orientation engine vs. radiator side when reinstalling the thermostat.