A PID is a glorified electronic thermostat on an e61, DB or HX. There is an offset, which varies with ambient conditions, between the set point and the brew temp. In my office I had to raise the DB boiler temp 3°F for the same group temperature when the summer heat arrived and the aircon is on. Ditto the HX PID at home.
On a pstat controlled HX, the groups will be too hot at idle and you can flush down to whatever temp you like. With Eric's adapter you can nail any temp desired on an HX. With practise, you can nail any temperature without it. Rather than focusing a number, think 'tastes right'. It's all about being able to repeat a routine.
Unless you have identical hardware, take vendor recommendations with a grain of salt. Learn how dose and temp affect a shot. With a new coffee either start at roaster suggestion or your own standard dose, temperature and brew ratio. Regardless of method chosen, you'll probabaly need to adjust for taste.
All of the machines listed are capable of great espresso. Choose the one you'll like to look at for several years.
IMC, Vibiemme. Twice
