I think Kirk in the 1st and 2nd season is very well defined. He is the classic human hero leader. A strong, ethical, decisive and impartial(mostly) man who is outwardly confident with a well controlled sense of self questioning.
In season 3 I feel the writing for Kirk (and the rest) was not up to the first 2 and I think we saw more of Shatner's personality to compensate.
For those who have read the Patrick O'Brien Aubrey/Maturin books, I think Jack Aubrey and James Kirk are almost the same character.
I asked my wife, a very casual TOS watcher, to describe Kirk in 3 words.
She chose Cool, Confident, and Horny.