It's not really "one person" who starts off with the ball BUT generally whoever the kicker is will technically start with kicking the ball to the opposition. The person on the field who gets the ball the most I would say would be the Fly Half or Scrum Half
the kicker, who is often the Fly Half (number 10) but occasionally the fullback (15) or the halfback (9), kicks off to the other team. he lets his team know where the ball is going so they can chase it, any player from the oposing team can catch it, but it normally tends to be a forward
fly half,scrum half,full back and hooker
usually the kicker and that can be anyone. but the game really starts with whoever catches it and the forwards usually get the ball off the kick
Occasionally the ref, who then gives it to a player.