A small rotation of good shirts is better than a rail of poor ones. These five cover almost everything.
White Oxford
The most useful shirt there is. It is right with a tweed jacket, with a blazer and tie, and on its own with chinos.
Pale blue poplin
Smoother and a little smarter. Blue flatters most skin tones and makes a navy suit look less severe than white does.
A fine stripe
A narrow blue or burgundy stripe adds interest under a plain jacket without competing with a tie.
Linen
For April to September. Buy it washed, so it is soft already, and do not fight the creases.
An evening shirt
A plain white poplin with a semi-spread collar and a covered or pearl-button front. Keep it for the nights that need it.
Buy shirts by collar size, not by letter. A collar that fits is the difference between a tie looking right and looking borrowed.