The type of oil used in a manual transmission depends entirely on the vehicle and its specifications. There's no single "correct" oil. The owner's manual is the definitive source for this information. It will specify the correct type, viscosity (like 75W-90, 75W-80, 80W-90, etc.), and often the API (American Petroleum Institute) classification or manufacturer's specification.
Using the wrong oil can severely damage the transmission. Don't rely on general advice – always check your owner's manual.