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 series, the first was Captain Jonathan Archer, second was James T Kirk and third was Jean-Luc Picard. But one cannot go purely by the main captains of the TV series, as Captain Pike was in the pilot episode before Kirk, and another captain was alluded to also during the original series of Star Trek.
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First is the Captain - Kirk
Second - Spock
Third - Scotty
How I know this; Every time Kirk left the Ship, Scotty is told to 'take the helm'
Fourth - McCoy
Fifth- Uhura
Sixth - Sulu
Seventh - Chekov (He's 17- 18 in the shows)
In the Original Star Trek the third in command of the USS Enterprise was Lt. Commander Montgomery Scott the Cheif Engineer
Ranked second in command aboard the Starship Enterprise in the Next Generation is Commander William T. Riker.
Mr. Spock (in the original series); Commander Riker (in the Next Generation series)
Mr Spock is the second-in-command of the Original Starship Enterprise, his rank is Commander. He also serves as the chief Science Officer.
The Starship Enterprise is a Space ship invented for the fictional world of Star Trek. To explore space and seek out new civilizations.
Dr. Smith
6
I'm a little embarrassed to admit that I know this, but Captain Jean-Luc Picard.