<h1>1 I recall that my first handshake, with the man who made this fantastic experience possible, was out of gratitude; my second was as a fellow competitor; my third as a winner.</h1>
<p>or</p>
<h1>2 My first handshake was the beginning, with the employer who made this experience possible. My second was a rite of passage, with the fellow competitor who recognized me as an equal. My third was the endI had proven myself a winner.</h1>
<p>Number 2 says more. It gets the point across clearly. Number 1 has some grammar issues, so if you do decide to use that one, you'd have to tweak it a little.</p>
<p>Why did not you have two or three handshakes with one person, with each handshake teaching you some special truth about life , or something ? It may be more concise and better developed.</p>