Just chiming in here as a health care professional.
The manual cuff with stethoscope will be the most accurate way to take a BP. This is assuming that the clinician has good technique with cuff placement and good hearing. (Although we also watch the needle on the gauge move) The start of the beating is the systolic or top number and the end of the beating is the diastolic number.
A digital arm cuff is generally pretty accurate for most people. There are exceptions including persons with arrhythmia such as AFib or persons with tremors such as with Parkinson’s disease. The digital cuff does not always differentiate between a muscle movement and a pulse at the sensor. It also frequently gives an error for very low BP readings.
The wrist cuff is the least accurate however can be very useful for home use especially if a person cannot apply an arm cuff independently (stroke patients for example) For some people it is actually quite accurate and is at least generally able to show a net change that should be checked out. We also often use it with patients with severe dementia because they can be very resistant to any compression on their arm.
Hope this helps. 