USS Enterprise was the world’s first nuclear powered aircraft carrier, and would see an exceptional five decades of active service throughout an astounding number of operations, including being the first nuclear powered ship to engage in combat. However, Enterprise’s deadliest day was not off of Vietnam, but off of Hawaii.
There is legitimate controversy over which ship was America’s first true battleship. But the Navy answers that question relatively clearly- USS Indiana was, from the outset, called "Battleship Number One."