Regarding to tap changer installation side, the applied voltage of power transformer is important.
Most power transformers have the tapping in the HV winding for two reasons. Firstly, it is convenient to assume that the purpose of the tapping is to compensate for variations in the applied voltage which, for most transformers, except generator transformers, will be to the HV winding.
As the applied voltage increases, more tapping turns are added to the HV winding by the tap changer so that the volts per turn remain constant, as does the LV winding output voltage. If the applied voltage is reduced, tapping turns are removed from the HV winding again keeping the volts per turn constant and so retaining constant LV voltage. From the transformer design point of view, the important aspect of this is that, since the volts per turn remains constant, so does the flux density. Hence the design flux density can be set at a reasonably high economic level without the danger of the transformer being driven into saturation due to supply voltage excursions.
The second reason for locating tapping on the HV side is that this winding carries the lower current so that the physical size of tapping leads is less and the tap changer itself carries less current.
Since the tapping are part of the HV winding and applied voltage side, frequently these can be arranged simply by bringing out the tapping leads at the appropriate point of the winding. This must, of course, coincide with the outer turn of a disc, but this can usually be arranged without undue difficulty.