Counting the first two versions (XCV 330 and NX-01) Captain James Tiberius Kirk would be third.
The third captain of the starship Enterprise is uncertain. If one goes purely by the television...
In the Original Star Trek Series Spok was Second in Command of the Enterprise NCC-1701. In Star Trek The Next Generation Commander Willaim T. Riker is the Second in Command/First Officer of the USS...