Which Ampere range and precision does my amperometer need to monitor a current of 220V between 50W and 300W
zero to 1.5A

Power, voltage and current are related by the equation P=IV. You know V=220volts and you want to measure up to 300W.  So the corresponding current is 1.36Amps.  An ammeter which can read up to 1.5 or 2A would work well.

The precision you want from the ammeter depends on the precision you want to measure the power with.  If you want to measure to the nearest watt, you need an ammeter that can measure to the nearest I=1W/220V=4.5mA.

Or...

You could buy a plug in power meter. These special meters are designed for measuring the power consumption of electronic devices.  You plug them into the wall, and then plug the computer into the socket of the front of the meter.  they are cheap, easy to use, safe, and give all the readings you might want, including power, average power, current, power factor etc.



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