My take on this is as follows. If you are starting off with a Classic, you need to understand the machine before you invest on PID's. First of all, the manufacturer's warranty will be invalidated by changing anything like this on the machine. So beware!.
The machine comes with 2 thermostats which control the temperature of the boiler. One is called the Coffee thermostat and the other Steam thermostat. Coffee Thermostat is fitted on the side of the boiler and the steam stat is fitted on the top of the boiler.
Coffee stat temperature ranges from about 70-72 degrees to 90-92 degrees. When you turn the machine on, the middle light comes on when the boiler reaches the lower temperature. It remains on until it reaches the higher level. It is always good to warm the portafilter before making your coffee.
Once you know the range and how the light turns on and off, you can decide when you want to press the button for coffee. I normally wait for the light to go off, ie when it has just reached the higher level, to press the coffee button to dispense the water through the coffee. Depending on the coffee that you are using you can try it at different temperatures. What a PID does is to allow you to narrow the range.
My advice is to learn using the machine at different levels of temperature before modifying the the machine.