Choosing sides for an ironclad wargame

Which navies would make the most useful opposing sides in a game about ironclads fighting one another?

Britain and France provide the strongest main pairing because they fielded the largest ironclad forces, with U.S. monitors adding a distinct third design tradition.

Britain and France are the most natural opposing sides because they possessed the two largest ironclad forces. Their competition gives a game enough ships for a sustained fleet comparison instead of a single isolated duel. The United States would add monitors and a markedly different design approach. This is a hypothetical game roster, and the answer makes no claim that such a three-sided war occurred.