Salamis Bay
Salamis
The first naval battle in history between aircraft carriers was the battle of the Coral Sea in 1942.
The Greek blocking force held the pass while the naval engagement in the adjacent strait at Artemesion began.
Battle of Midway.
I don't know about major, but the first naval battle in the historical record was Hittites defeat Cypriots near Cyprus
The Battle of Hampton Roads.
The first naval battle of the Civil War happened on April 13, 1861. This naval battle took place at Fort Sumter.
It was the first naval battle between two ironclads.
The Greek fleet lost the naval battle of Artemesion to the Persians. As the defence of the Thermopylai pass had been to force the naval battle, the force holding the pass was withdrawn as having no further purpost. A second successful sea battle was fought at Salamis.
Fort Sumter
There was no Salamis war. There was a naval battle of Salamis which was part of the Greek strategy to repel the Persian invasion of the Greek mainland in 480 BCE.
Battle of Midway