Besides the extent of the map, you also have to consider the purpose of the map. Different kinds of distortion are more or less appropriate depending on what the map is for. Is it a thematic (displaying a particular data set like weather or population), navigational (for getting from A to B) or reference map (For giving an overview of general information). You also need to consider the level of sophistication of the notional cartographer and the data available to them. Modern global reference maps use quite sophisticated projections that look decidedly "modern" (Winkel Tripel and Robinson in particular)

Whatever the projection, you will have to understand the particular distortion created by it so that you can draw that distortion into the map.