The Robinson projection is probably what you're looking for. It was explicitly created to try to balance these two extremes. I also think that the Robinson is

The Robinson projection is probably what you're looking for. It was explicitly created to try to balance these two extremes. I also think that the Robinson is probably the best candidate for an accurate "default" map of the world. There are projections I prefer but the Robinson retains the recognizablity as being obviously a map of the world.